Step |
Hyp |
Ref |
Expression |
1 |
|
rexima.x |
|- ( x = ( F ` y ) -> ( ph <-> ps ) ) |
2 |
|
fvexd |
|- ( ( ( F Fn A /\ B C_ A ) /\ y e. B ) -> ( F ` y ) e. _V ) |
3 |
|
fvelimab |
|- ( ( F Fn A /\ B C_ A ) -> ( x e. ( F " B ) <-> E. y e. B ( F ` y ) = x ) ) |
4 |
|
eqcom |
|- ( ( F ` y ) = x <-> x = ( F ` y ) ) |
5 |
4
|
rexbii |
|- ( E. y e. B ( F ` y ) = x <-> E. y e. B x = ( F ` y ) ) |
6 |
3 5
|
bitrdi |
|- ( ( F Fn A /\ B C_ A ) -> ( x e. ( F " B ) <-> E. y e. B x = ( F ` y ) ) ) |
7 |
1
|
adantl |
|- ( ( ( F Fn A /\ B C_ A ) /\ x = ( F ` y ) ) -> ( ph <-> ps ) ) |
8 |
2 6 7
|
ralxfr2d |
|- ( ( F Fn A /\ B C_ A ) -> ( A. x e. ( F " B ) ph <-> A. y e. B ps ) ) |