Metamath Proof Explorer


Theorem dmexd

Description: The domain of a set is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypothesis dmexd.1
|- ( ph -> A e. V )
Assertion dmexd
|- ( ph -> dom A e. _V )

Proof

Step Hyp Ref Expression
1 dmexd.1
 |-  ( ph -> A e. V )
2 dmexg
 |-  ( A e. V -> dom A e. _V )
3 1 2 syl
 |-  ( ph -> dom A e. _V )