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Definition df-ac 8493
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 8835 as our definition, because the equivalence to more standard forms (dfac2 8507) 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 8835 itself as dfac0 8509. (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 8492 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1378 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1378 . . . . . 6  class  x
63, 5wss 3476 . . . . 5  wff  f  C_  x
75cdm 4999 . . . . . 6  class  dom  x
83, 7wfn 5581 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 369 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1596 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1377 . 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  8498  ac7  8849
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