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Definition df-ac 9609
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 9952 as our definition, because the equivalence to more standard forms (dfac2 9624) 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 9952 itself as dfac0 9626. (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 9608 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1541 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1541 . . . . . 6 class 𝑥
63, 5wss 3841 . . . . 5 wff 𝑓𝑥
75cdm 5519 . . . . . 6 class dom 𝑥
83, 7wfn 6328 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 399 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1786 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1540 . 2 wff 𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
121, 11wb 209 1 wff (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  9614  ac7  9966  fineqvac  32629
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