تاريخ الفحص في شهادة السلامة.

Not really. It is a noun phrase, not a full sentence with a verb.

In context, this kind of phrase is very common as a label, heading, or form field, like:

• inspection date on the safety certificate
• date of inspection in the safety certificate

Arabic often uses short noun phrases like this on documents instead of full sentences.

Because Arabic usually expresses of with the iḍāfa construction, also called the construct phrase.

So:

• تاريخ الفحص = date of the inspection
• شهادة السلامة = certificate of safety or safety certificate

In an iḍāfa, Arabic simply puts two nouns next to each other:

• the first noun is the main thing
• the second noun specifies it

So instead of saying date of inspection with a separate word for of, Arabic says literally date the-inspection.

Because تاريخ is the first noun in an iḍāfa, and the first noun in an iḍāfa normally does not take الـ.

So you get:

• تاريخ الفحص and not التاريخ الفحص

The whole phrase can still be definite because the second noun is definite:

• الفحص = the inspection

That makes تاريخ الفحص definite as a whole: the inspection date.

The same thing happens in:

• شهادة السلامة

Here شهادة has no الـ, but the phrase is definite because السلامة is definite.

It contains two iḍāfa phrases plus a preposition:

1. تاريخ الفحص
   = an iḍāfa: date of the inspection

2. في شهادة السلامة
   = in/on the safety certificate

Inside that prepositional phrase, شهادة السلامة is another iḍāfa:

• شهادة = certificate
• السلامة = safety
• together: safety certificate or certificate of safety

So the structure is roughly:

• [تاريخ الفحص] [في شهادة السلامة]
• [inspection date] [in/on the safety certificate]

في basically means in, but in English the most natural translation depends on context.

With documents, fields, and forms, English may say:

• in
• on

So في شهادة السلامة could be understood as:

• in the safety certificate
• on the safety certificate

Arabic uses في more broadly than English sometimes does, so the best English preposition depends on what sounds natural in context.

Because ة is tāʾ marbūṭa, and its pronunciation changes depending on context.

• In pause, by itself, شهادة is usually pronounced shahāda(h)
• But when it is followed by another word in an iḍāfa, the t sound appears

So in:

• شهادة السلامة

it is pronounced more like:

• shahādat as-salāmah

This is very common in Arabic. The same thing happens in phrases like:

• مدينة القاهرة → madīnat al-Qāhira

Because س is a sun letter.

When الـ comes before a sun letter, the l sound of الـ is not pronounced separately. Instead, the following consonant is doubled.

So:

• السلامة is written with الـ
• but pronounced as-salāmah

By contrast, in الفحص, the letter ف is a moon letter, so the l is pronounced:

• al-faḥṣ

So the phrase sounds like:

• tārīkh al-faḥṣ fī shahādat as-salāmah

In careful fully vocalized MSA, as a standalone heading, it would commonly be:

• تاريخُ الفحصِ في شهادةِ السلامةِ

Here is why:

• تاريخُ: nominative, as the head of the phrase
• الفحصِ: genitive, because it is the second term of an iḍāfa
• شهادةِ: genitive, because it comes after في
• السلامةِ: genitive, because it is the second term of another iḍāfa

In everyday reading and most real-life writing, these case endings are usually not written and often not pronounced.

Because Arabic usually puts the main noun first and the specifying noun after it in an iḍāfa.

So:

• تاريخ الفحص = literally date of the inspection
• not inspection date in the English order

English often uses a noun before another noun, as in inspection date. Arabic normally does not do that here. Instead, it uses the construct phrase:

• main item first
• descriptor after it

This is one of the most important word-order differences between English and Arabic noun phrases.

A practical pronunciation is:

• tārīkh al-faḥṣ fī shahādat as-salāmah

A few helpful notes:

• تاريخ = tārīkh
• الفحص = al-faḥṣ
• ح in فحص is the deeper ḥ sound, not the English h
• شهادة in this phrase is shahādat, with a pronounced t
• السلامة is as-salāmah because of sun-letter assimilation

If you want a more careful grammatical pronunciation with case endings, it would be closer to:

• tārīkhu l-faḥṣi fī shahādati s-salāmah

But for most learners, the simpler pronunciation is enough at first.