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Definition df-ac 9872
Description: The expression CHOICE will be used as a readable shorthand for any form of the axiom of choice; all concrete forms are long, cryptic, have dummy variables, or all three, making it useful to have a short name. Similar to the Axiom of Choice (first form) of [Enderton] p. 49.

There is a slight problem with taking the exact form of ax-ac 10215 as our definition, because the equivalence to more standard forms (dfac2 9887) requires the Axiom of Regularity, which we often try to avoid. Thus, we take the first of the "textbook forms" as the definition and derive the form of ax-ac 10215 itself as dfac0 9889. (Contributed by Mario Carneiro, 22-Feb-2015.)

Assertion
Ref Expression
df-ac (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Distinct variable group:   𝑥,𝑓

Detailed syntax breakdown of Definition df-ac
StepHypRef Expression
1 wac 9871 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1538 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1538 . . . . . 6 class 𝑥
63, 5wss 3887 . . . . 5 wff 𝑓𝑥
75cdm 5589 . . . . . 6 class dom 𝑥
83, 7wfn 6428 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 396 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1782 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1537 . 2 wff 𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
121, 11wb 205 1 wff (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  9877  ac7  10229  fineqvac  33066
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