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Axiom ax-cc 8366
Description: The axiom of countable choice (CC), also known as the axiom of denumerable choice. It is clearly a special case of ac5 8408, but is weak enough that it can be proven using DC (see axcc 8389). 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 1653 . . 3
3 com 4886 . . 3
4 cen 7155 . . 3
52, 3, 4wbr 4243 . 2
6 vz . . . . . . 7
76cv 1653 . . . . . 6
8 c0 3616 . . . . . 6
97, 8wne 2606 . . . . 5
10 vf . . . . . . . 8
1110cv 1653 . . . . . . 7
127, 11cfv 5501 . . . . . 6
1312, 7wcel 1728 . . . . 5
149, 13wi 4 . . . 4
1514, 6, 2wral 2712 . . 3
1615, 10wex 1551 . 2
175, 16wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  axcc2lem  8367
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