Theorem tz6.12-1-afv

Description: Function value (Theorem 6.12(1) of TakeutiZaring p. 27, analogous to tz6.12-1 . (Contributed by Alexander van der Vekens, 29-Nov-2017)

	Ref	Expression
Assertion	tz6.12-1-afv	|- ( ( A F y /\ E! y A F y ) -> ( F ''' A ) = y )

Proof

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-afv	|- ( ( <. 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 )