Metamath Proof Explorer


Theorem fndmexb

Description: The domain of a function is a set iff the function is a set. (Contributed by AV, 8-Aug-2024)

Ref Expression
Assertion fndmexb F Fn A A V F V

Proof

Step Hyp Ref Expression
1 fnex F Fn A A V F V
2 1 ex F Fn A A V F V
3 simpr F Fn A F V F V
4 simpl F Fn A F V F Fn A
5 3 4 fndmexd F Fn A F V A V
6 5 ex F Fn A F V A V
7 2 6 impbid F Fn A A V F V