Description: Function value (Theorem 6.12(1) of TakeutiZaring p. 27), analogous to tz6.12-1 . (Contributed by AV, 5-Sep-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | tz6.12-1-afv2 | |- ( ( A F y /\ E! y A F y ) -> ( F '''' A ) = y ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br | |- ( A F y <-> <. A , y >. e. F ) |
|
2 | 1 | eubii | |- ( E! y A F y <-> E! y <. A , y >. e. F ) |
3 | tz6.12-afv2 | |- ( ( <. A , y >. e. F /\ E! y <. A , y >. e. F ) -> ( F '''' A ) = y ) |
|
4 | 1 2 3 | syl2anb | |- ( ( A F y /\ E! y A F y ) -> ( F '''' A ) = y ) |