Metamath Proof Explorer


Theorem ac8

Description: An Axiom of Choice equivalent. Given a family x of mutually disjoint nonempty sets, there exists a set y containing exactly one member from each set in the family. Theorem 6M(4) of Enderton p. 151. (Contributed by NM, 14-May-2004)

Ref Expression
Assertion ac8 zxzzxwxzwzw=yzx∃!vvzy

Proof

Step Hyp Ref Expression
1 dfac5 CHOICExzxzzxwxzwzw=yzx∃!vvzy
2 1 axaci zxzzxwxzwzw=yzx∃!vvzy