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Definition df-ac 8495
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 8837 as our definition, because the equivalence to more standard forms (dfac2 8509) 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 8837 itself as dfac0 8511. (Contributed by Mario Carneiro, 22-Feb-2015.)

Assertion
Ref Expression
df-ac  |-  (CHOICE  <->  A. x E. f ( f  C_  x  /\  f  Fn  dom  x ) )
Distinct variable group:    x, f

Detailed syntax breakdown of Definition df-ac
StepHypRef Expression
1 wac 8494 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1380 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1380 . . . . . 6  class  x
63, 5wss 3458 . . . . 5  wff  f  C_  x
75cdm 4985 . . . . . 6  class  dom  x
83, 7wfn 5569 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 369 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1597 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1379 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 184 1  wff  (CHOICE  <->  A. x E. f ( f  C_  x  /\  f  Fn  dom  x ) )
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  8500  ac7  8851
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