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Definition df-ac 8560
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 8902 as our definition, because the equivalence to more standard forms (dfac2 8574) 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 8902 itself as dfac0 8576. (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 8559 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1437 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1437 . . . . . 6  class  x
63, 5wss 3442 . . . . 5  wff  f  C_  x
75cdm 4859 . . . . . 6  class  dom  x
83, 7wfn 5602 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 371 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1658 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1436 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 188 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  8565  ac7  8916
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