Con el justificante del pago, puedo demostrar que ya he pagado la matrícula.

Here, justificante means a document that proves something. In this sentence, it is proof that the payment has been made.

In Spain, justificante is a very common word in administrative and banking contexts. It can be:

• a bank transfer confirmation
• a stamped payment form
• a receipt
• any document you can show as evidence

So it is a bit broader than just receipt.

Del is simply the contraction of de + el.

So:

• del pago = de el pago

Both justificante del pago and justificante de pago are possible.

A useful difference:

• justificante de pago sounds more like a standard label or type of document
• justificante del pago points more to a specific payment

In real life, especially in Spain, justificante de pago is very common, but justificante del pago is also correct.

Here, con shows the means or evidence used to do something.

So Con el justificante del pago means something like:

• using the proof of payment
• with the proof of payment
• by means of the proof of payment

It tells you what the speaker can use in order to prove the statement.

That phrase is placed at the beginning for emphasis. It highlights the evidence first.

The sentence could also be reordered:

• Puedo demostrar que ya he pagado la matrícula con el justificante del pago.

But starting with Con el justificante del pago makes it clearer that this is the proof or tool being used.

It is a very natural word order in Spanish when you want to foreground the method, evidence, or circumstance.

The comma separates the introductory phrase from the main clause.

Structure:

• Con el justificante del pago, = introductory prepositional phrase
• puedo demostrar que ya he pagado la matrícula = main clause

In Spanish, with a fronted phrase like this, the comma is often used to mark a pause, especially when the introductory part is not very short. It helps readability, though with shorter phrases Spanish is sometimes more flexible about whether to include the comma.

After demostrar, Spanish often uses que + clause to say what is being proved.

So:

• puedo demostrar que ya he pagado la matrícula

means the speaker can prove the fact expressed in the clause after que.

This is very normal Spanish. Compare:

• Sé que...
• Creo que...
• Veo que...
• Demuestro que...

If the idea is already understood, Spanish can also use a pronoun:

• Puedo demostrarlo.

This is a very important Spain-Spanish point.

In Spain, the present perfect is often used for past actions that are still relevant now:

• ya he pagado

That fits well here because the payment matters in the present: the speaker can now prove it.

In much of Latin America, people would very often say:

• ya pagué

In Spain, ya pagué is also possible in some contexts, but ya he pagado is especially natural when the past action has a clear connection to the present situation.

Ya means already.

It adds the idea that the payment is completed before the current moment, often with the nuance:

• this has been done
• there is no need to wait
• the matter is settled

Without ya, the sentence would still be grammatical:

• puedo demostrar que he pagado la matrícula

But ya makes the completion more explicit.

Because the speaker is stating a fact they can prove.

After demostrar que, Spanish normally uses the indicative, since the content is presented as real and verifiable:

• demostrar que ya he pagado

The subjunctive is generally used for doubt, unreality, emotion, purpose, and similar meanings. None of that applies here.

So:

• puedo demostrar que ya he pagado = correct
• a subjunctive form here would sound wrong

In this context, la matrícula refers to the enrolment or registration fee, often in a school or university setting.

In Spain, matrícula can mean different things depending on context:

• registration / enrolment
• registration fee / tuition-related fee
• vehicle number plate

Here, because the sentence talks about paying it, la matrícula is clearly the academic fee or enrolment payment.

The article la shows that this is a specific, known fee or enrolment.

Spanish often uses the definite article where English might use a possessive or no article at all. So instead of saying something like my enrolment fee, Spanish often just says:

• la matrícula

when the context already makes clear which one is meant.

Not really. Spanish often allows this kind of repetition if it keeps the sentence clear.

Here:

• justificante del pago
• he pagado la matrícula

This is perfectly natural.

If you wanted to avoid repetition, you could say:

• Con el justificante, puedo demostrar que ya he pagado la matrícula.
• Con el justificante del pago, puedo demostrarlo.
• Con el justificante, puedo demostrar que ya la he pagado.

But the original sentence is completely fine.

Yes, but the nuance changes a little.

Possible alternatives:

• recibo = receipt
• comprobante = proof / voucher
• resguardo = receipt slip / proof document
• acuse in some specific administrative contexts

For Spain specifically:

• justificante is very common and natural in formal or administrative language
• recibo is also common, but it sounds more specifically like a receipt
• comprobante is understood, but it is less characteristically Spain-Spanish than justificante

So justificante is an excellent choice here.