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 ) |
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 ) |