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Definition df-ac 8795
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 9137 as our definition, because the equivalence to more standard forms (dfac2 8809) 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 9137 itself as dfac0 8811. (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 8794 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1473 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1473 . . . . . 6 class 𝑥
63, 5wss 3535 . . . . 5 wff 𝑓𝑥
75cdm 5024 . . . . . 6 class dom 𝑥
83, 7wfn 5781 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 382 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1694 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1472 . 2 wff 𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
121, 11wb 194 1 wff (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  8800  ac7  9151
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