Theorem ac6s3

Description: Generalization of the Axiom of Choice to classes. Theorem 10.46 of TakeutiZaring p. 97. (Contributed by NM, 3-Nov-2004)

	Ref	Expression
Hypotheses	ac6s.1	|- A e. _V
	ac6s.2	|- ( y = ( f ` x ) -> ( ph <-> ps ) )
Assertion	ac6s3	|- ( A. x e. A E. y ph -> E. f A. x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		ac6s.1	|- A e. _V
2		ac6s.2	|- ( y = ( f ` x ) -> ( ph <-> ps ) )
3	1 2	ac6s2	|- ( A. x e. A E. y ph -> E. f ( f Fn A /\ A. x e. A ps ) )
4		exsimpr	|- ( E. f ( f Fn A /\ A. x e. A ps ) -> E. f A. x e. A ps )
5	3 4	syl	|- ( A. x e. A E. y ph -> E. f A. x e. A ps )