Páka je proti dveřím.

Because proti requires the dative case in Czech.

• basic form: dveře = door / doors
• after proti: dveřím = dative

So:

• Páka je proti dveřím.

is using the correct case after proti.

Dveře is a plural-only noun in Czech. This is called pluralia tantum.

That means Czech treats door as grammatically plural, even when English uses singular door.

So you get forms like:

• nominative: dveře
• dative: dveřím
• instrumental: dveřmi

This is normal and very common in Czech.

Here proti means something like:

• against
• opposite
• facing

The exact English translation depends on context.

With a physical object, proti often shows position in relation to something else. In this sentence, it describes where the lever is relative to the door.

Also remember: proti is a preposition that takes the dative case.

Páka is a feminine noun in the nominative singular.

In this sentence it is the subject:

• Páka = the lever / handle
• je = is
• proti dveřím = against/opposite the door

So páka is the thing being described.

Je is the 3rd person singular form of the verb být (to be).

So:

• je = is

In this sentence:

• Páka je proti dveřím.
• The lever is against/opposite the door.

Czech does not use articles like English a/an/the.

So páka can mean:

• a lever
• the lever

and dveřím can mean:

• to a door
• to the door

The exact meaning comes from the context, not from an article.

Yes. Czech word order is more flexible than English.

The neutral order here is:

• Páka je proti dveřím.

But other orders are possible, for example:

• Proti dveřím je páka.

This might sound more marked or emphasize the location first.

Even though the word order can change, the case endings still show the grammatical relationships.

Because of the case endings.

• páka is in the nominative, which is the usual case for the subject
• dveřím is in the dative, required by proti

So Czech grammar tells you:

• páka = subject
• dveřím = object of the preposition

Roughly:

• dveh-rzheem

A few notes:

• dv at the start is pronounced together
• ě affects the preceding consonant
• ř is the famous Czech sound that does not exist in English; learners often approximate it as something like rzh
• í is a long ee sound

You do not need a perfect ř right away to be understood; an approximation is normal for learners.

Yes, in standard Czech proti takes the dative case.

Examples:

• proti zdi = against the wall
• proti škole = opposite the school
• proti větru = against the wind
• proti dveřím = against/opposite the door

So if you see proti, you should expect a dative form after it.