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Axiom ax-cc 8486
Description: The axiom of countable choice (CC), also known as the axiom of denumerable choice. It is clearly a special case of ac5 8528, but is weak enough that it can be proven using DC (see axcc 8509). 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 1669 . . 3
3 com 6486 . . 3
4 cen 7270 . . 3
52, 3, 4wbr 4318 . 2
6 vz . . . . . . 7
76cv 1669 . . . . . 6
8 c0 3673 . . . . . 6
97, 8wne 2652 . . . . 5
10 vf . . . . . . . 8
1110cv 1669 . . . . . . 7
127, 11cfv 5438 . . . . . 6
1312, 7wcel 1732 . . . . 5
149, 13wi 4 . . . 4
1514, 6, 2wral 2759 . . 3
1615, 10wex 1565 . 2
175, 16wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  axcc2lem  8487
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