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Definition df-ac 8822
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 9164 as our definition, because the equivalence to more standard forms (dfac2 8836) 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 9164 itself as dfac0 8838. (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 8821 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1474 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1474 . . . . . 6 class 𝑥
63, 5wss 3540 . . . . 5 wff 𝑓𝑥
75cdm 5038 . . . . . 6 class dom 𝑥
83, 7wfn 5799 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 383 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1695 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1473 . 2 wff 𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
121, 11wb 195 1 wff (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  8827  ac7  9178
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