Theorem ac6s4

Description: Generalization of the Axiom of Choice to proper classes. B is a collection B ( x ) of nonempty, possible proper classes. (Contributed by NM, 29-Sep-2006)

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

Proof

Step	Hyp	Ref	Expression
1		ac6s4.1	|- A e. _V
2		n0	|- ( B =/= (/) <-> E. y y e. B )
3	2	ralbii	|- ( A. x e. A B =/= (/) <-> A. x e. A E. y y e. B )
4		eleq1	|- ( y = ( f ` x ) -> ( y e. B <-> ( f ` x ) e. B ) )
5	1 4	ac6s2	|- ( A. x e. A E. y y e. B -> E. f ( f Fn A /\ A. x e. A ( f ` x ) e. B ) )
6	3 5	sylbi	|- ( A. x e. A B =/= (/) -> E. f ( f Fn A /\ A. x e. A ( f ` x ) e. B ) )