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Definition df-acn 8344
Description: Define a local and length-limited version of the axiom of choice. The definition of the predicate is that for all families of nonempty subsets of indexed on (i.e. functions A-->~P \{ }), there is a function which selects an element from each set in the family. (Contributed by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
df-acn
Distinct variable group:   , , , ,

Detailed syntax breakdown of Definition df-acn
StepHypRef Expression
1 cA . . 3
21wacn 8340 . 2
3 cvv 3109 . . . . 5
41, 3wcel 1818 . . . 4
5 vy . . . . . . . . . 10
65cv 1394 . . . . . . . . 9
7 vg . . . . . . . . . 10
87cv 1394 . . . . . . . . 9
96, 8cfv 5593 . . . . . . . 8
10 vf . . . . . . . . . 10
1110cv 1394 . . . . . . . . 9
126, 11cfv 5593 . . . . . . . 8
139, 12wcel 1818 . . . . . . 7
1413, 5, 1wral 2807 . . . . . 6
1514, 7wex 1612 . . . . 5
16 vx . . . . . . . . 9
1716cv 1394 . . . . . . . 8
1817cpw 4012 . . . . . . 7
19 c0 3784 . . . . . . . 8
2019csn 4029 . . . . . . 7
2118, 20cdif 3472 . . . . . 6
22 cmap 7439 . . . . . 6
2321, 1, 22co 6296 . . . . 5
2415, 10, 23wral 2807 . . . 4
254, 24wa 369 . . 3
2625, 16cab 2442 . 2
272, 26wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  acnrcl  8444  acneq  8445  isacn  8446
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