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Definition df-ac 8924
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 9266 as our definition, because the equivalence to more standard forms (dfac2 8938) 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 9266 itself as dfac0 8940. (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 8923 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1480 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1480 . . . . . 6 class 𝑥
63, 5wss 3567 . . . . 5 wff 𝑓𝑥
75cdm 5104 . . . . . 6 class dom 𝑥
83, 7wfn 5871 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 384 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1702 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1479 . 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  8929  ac7  9280
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