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

Step	Hyp	Ref	Expression
1		vx	. . . 4
2	1	cv 1394	. . 3
3		com 6700	. . 3
4		cen 7533	. . 3
5	2, 3, 4	wbr 4452	. 2
6		vz	. . . . . . 7
7	6	cv 1394	. . . . . 6
8		c0 3784	. . . . . 6
9	7, 8	wne 2652	. . . . 5
10		vf	. . . . . . . 8
11	10	cv 1394	. . . . . . 7
12	7, 11	cfv 5593	. . . . . 6
13	12, 7	wcel 1818	. . . . 5
14	9, 13	wi 4	. . . 4
15	14, 6, 2	wral 2807	. . 3
16	15, 10	wex 1612	. 2
17	5, 16	wi 4	1

This axiom is referenced by:  axcc2lem  8837