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Definition df-ac 10153
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 10496 as our definition, because the equivalence to more standard forms (dfac2 10169) 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 10496 itself as dfac0 10171. (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 10152 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1535 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1535 . . . . . 6 class 𝑥
63, 5wss 3962 . . . . 5 wff 𝑓𝑥
75cdm 5688 . . . . . 6 class dom 𝑥
83, 7wfn 6557 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 395 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1775 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1534 . 2 wff 𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
121, 11wb 206 1 wff (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  10158  ac7  10510  fineqvac  35089
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