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Axiom ax-cc 8429
Description: The axiom of countable choice (CC), also known as the axiom of denumerable choice. It is clearly a special case of ac5 8471, but is weak enough that it can be proven using DC (see axcc 8452). It is, however, strictly stronger than ZF and cannot be proven in ZF. It states that any countable collection of non-empty sets must have a choice function. (Contributed by Mario Carneiro, 9-Feb-2013.)
Assertion
Ref Expression
ax-cc
Distinct variable group:   , ,

Detailed syntax breakdown of Axiom ax-cc
StepHypRef Expression
1 vx . . . 4
21cv 1661 . . 3
3 com 6441 . . 3
4 cen 7218 . . 3
52, 3, 4wbr 4302 . 2
6 vz . . . . . . 7
76cv 1661 . . . . . 6
8 c0 3660 . . . . . 6
97, 8wne 2644 . . . . 5
10 vf . . . . . . . 8
1110cv 1661 . . . . . . 7
127, 11cfv 5417 . . . . . 6
1312, 7wcel 1724 . . . . 5
149, 13wi 4 . . . 4
1514, 6, 2wral 2751 . . 3
1615, 10wex 1557 . 2
175, 16wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  axcc2lem  8430
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