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Definition df-ac 8573
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 8915 as our definition, because the equivalence to more standard forms (dfac2 8587) 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 8915 itself as dfac0 8589. (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 8572 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1454 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1454 . . . . . 6  class  x
63, 5wss 3416 . . . . 5  wff  f  C_  x
75cdm 4853 . . . . . 6  class  dom  x
83, 7wfn 5596 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 375 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1674 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1453 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 189 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  8578  ac7  8929
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