zhè zhèngmíng wǎngluò bù wěndìng.

A helpful way to parse it is:

• 这 = this
• 证明 = proves / shows
• 网络 = the network
• 不稳定 = not stable / unstable

So the structure is:

这 + 证明 + 网络不稳定
= This proves (that) the network is unstable.

In grammar terms:

• 这 is the subject
• 证明 is the verb
• 网络不稳定 is the thing being proved

Chinese often puts things together more directly than English does.

Yes. In this sentence, 这 means this, and 证明 means prove or show.

So:

• 这证明... = This proves...

Very often in Chinese, 这 can refer to a situation, fact, or evidence that was just mentioned before. It does not have to point to a physical object only.

For example, if someone says the connection dropped three times, you might say:

• 这证明网络不稳定。
• This proves the network is unstable.

Because Chinese often does not need an explicit word for that in this kind of sentence.

English says:

• This proves that the network is unstable.

Chinese simply says:

• 这证明网络不稳定。

The clause 网络不稳定 directly follows 证明. This is very natural in Chinese.

So even though English usually includes that, Chinese often leaves it out.

This is a very common question.

In Chinese, adjectives can often function as predicates by themselves. So:

• 网络稳定 = the network is stable
• 网络不稳定 = the network is not stable / the network is unstable

You do not usually need 是 before an adjective in this kind of sentence.

So:

• 网络是不稳定 is generally not the normal form here
• 网络不稳定 is the natural form

A good rule of thumb is:

• 是 is commonly used before nouns
• adjectives often do not need 是

It can be understood as either, depending on how natural the English translation is.

• 不 = not
• 稳定 = stable

So literally it is not stable, but in natural English that often becomes unstable.

Both ideas are correct. The Chinese form is transparent:

• 稳定 = stable
• 不稳定 = unstable / not stable

This is a very common pattern in Chinese: 不 + adjective.

Here it is pronounced bù.

That is because 不 changes to bú only when the following syllable has a fourth tone.

In this sentence:

• 不稳定
• 稳 is wěn, which is a third tone

So the pronunciation stays:

• bù wěndìng

Compare:

• 不是 = bú shì because 是 is fourth tone
• 不稳定 = bù wěndìng because 稳 is third tone

Here, 证明 is a verb meaning to prove or to show.

So in:

• 这证明网络不稳定。

it means:

• This proves/shows that the network is unstable.

Yes, 证明 can also be used as a noun in some contexts, meaning proof or certificate/documentary proof, depending on the situation.

Examples:

• 这能证明他的说法。 = This can prove his claim.
• 你有证明吗？ = Do you have proof / documentation?

So Chinese words are often flexible, and the sentence context tells you how the word is functioning.

网络 literally means network.

Depending on context, it can refer to:

• a computer network
• the internet
• a phone/data network
• a connection system more generally

In this sentence, it most likely means the network connection or the internet/network service.

So 网络不稳定 usually means something like:

• the network is unstable
• the internet connection is unstable
• the connection is unreliable

The exact English wording depends on the situation.

Yes, you can.

Both of these are possible:

• 这证明网络不稳定。
• 这证明了网络不稳定。

Adding 了 after 证明 can make the action sound more completed or more clearly established.

Very roughly:

• 这证明网络不稳定。 = This proves the network is unstable.
• 这证明了网络不稳定。 = This has proven / clearly proved that the network is unstable.

In many contexts, both are natural. The version without 了 is slightly more neutral and concise.

Yes. Depending on context, you might also see:

• 这说明网络不稳定。
• 这表明网络不稳定。

These are similar to 这证明网络不稳定, but the tone is a little different:

• 证明 = prove
• 说明 = explain / show
• 表明 = indicate / demonstrate

证明 can sound a bit stronger, as if there is solid evidence.
说明 and 表明 can sound a little less absolute, depending on context.

It is fairly neutral and can fit both spoken and written Chinese.

• 网络 and 稳定 are standard vocabulary.
• 证明 is also standard and natural.

In very casual speech, people might say something more conversational, such as:

• 这说明网络有点不稳定。
• 看来网络不太稳定。

But 这证明网络不稳定 is perfectly normal, especially when someone wants to sound clear and logical.