Theorem ac6s5

Description: Generalization of the Axiom of Choice to proper classes. B is a collection B ( x ) of nonempty, possible proper classes. Remark after Theorem 10.46 of TakeutiZaring p. 98. (Contributed by NM, 27-Mar-2006)

	Ref	Expression
Hypothesis	ac6s4.1	|- A e. _V
Assertion	ac6s5	|- ( A. x e. A B =/= (/) -> E. f A. x e. A ( f ` x ) e. B )

Proof

Step	Hyp	Ref	Expression
1		ac6s4.1	|- A e. _V
2	1	ac6s4	|- ( A. x e. A B =/= (/) -> E. f ( f Fn A /\ A. x e. A ( f ` x ) e. B ) )
3		exsimpr	|- ( E. f ( f Fn A /\ A. x e. A ( f ` x ) e. B ) -> E. f A. x e. A ( f ` x ) e. B )
4	2 3	syl	|- ( A. x e. A B =/= (/) -> E. f A. x e. A ( f ` x ) e. B )