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Definition df-ac 9150
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 9494 as our definition, because the equivalence to more standard forms (dfac2 9165) 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 9494 itself as dfac0 9168. (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 9149 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1631 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1631 . . . . . 6 class 𝑥
63, 5wss 3716 . . . . 5 wff 𝑓𝑥
75cdm 5267 . . . . . 6 class dom 𝑥
83, 7wfn 6045 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 383 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1853 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1630 . 2 wff 𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
121, 11wb 196 1 wff (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  9155  ac7  9508
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