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Definition df-ac 9232
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 9576 as our definition, because the equivalence to more standard forms (dfac2 9247) 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 9576 itself as dfac0 9250. (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 9231 . 2 wff CHOICE
2 vf . . . . . . 7 setvar 𝑓
32cv 1636 . . . . . 6 class 𝑓
4 vx . . . . . . 7 setvar 𝑥
54cv 1636 . . . . . 6 class 𝑥
63, 5wss 3780 . . . . 5 wff 𝑓𝑥
75cdm 5324 . . . . . 6 class dom 𝑥
83, 7wfn 6106 . . . . 5 wff 𝑓 Fn dom 𝑥
96, 8wa 384 . . . 4 wff (𝑓𝑥𝑓 Fn dom 𝑥)
109, 2wex 1859 . . 3 wff 𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
1110, 4wal 1635 . 2 wff 𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥)
121, 11wb 197 1 wff (CHOICE ↔ ∀𝑥𝑓(𝑓𝑥𝑓 Fn dom 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  9237  ac7  9590
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