Metamath Proof Explorer


Theorem elfvex

Description: If a function value has a member, then the argument is a set. (An artifact of our function value definition.) (Contributed by Mario Carneiro, 6-Nov-2015)

Ref Expression
Assertion elfvex
|- ( A e. ( F ` B ) -> B e. _V )

Proof

Step Hyp Ref Expression
1 elfvdm
 |-  ( A e. ( F ` B ) -> B e. dom F )
2 1 elexd
 |-  ( A e. ( F ` B ) -> B e. _V )