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Axiom ax-cc 8836
 Description: The axiom of countable choice (CC), also known as the axiom of denumerable choice. It is clearly a special case of ac5 8878, but is weak enough that it can be proven using DC (see axcc 8859). It is, however, strictly stronger than ZF and cannot be proven in ZF. It states that any countable collection of nonempty 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 1394 . . 3
3 com 6700 . . 3
4 cen 7533 . . 3
52, 3, 4wbr 4452 . 2
6 vz . . . . . . 7
76cv 1394 . . . . . 6
8 c0 3784 . . . . . 6
97, 8wne 2652 . . . . 5
10 vf . . . . . . . 8
1110cv 1394 . . . . . . 7
127, 11cfv 5593 . . . . . 6
1312, 7wcel 1818 . . . . 5
149, 13wi 4 . . . 4
1514, 6, 2wral 2807 . . 3
1615, 10wex 1612 . 2
175, 16wi 4 1
 Colors of variables: wff setvar class This axiom is referenced by:  axcc2lem  8837
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