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Definition df-ac 7627
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 7969 as our definition, because the equivalence to more standard forms (dfac2 7641) 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 7969 itself as dfac0 7643. (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 7626 . 2  wff CHOICE
2 vf . . . . . . 7  set  f
32cv 1618 . . . . . 6  class  f
4 vx . . . . . . 7  set  x
54cv 1618 . . . . . 6  class  x
63, 5wss 3078 . . . . 5  wff  f  C_  x
75cdm 4580 . . . . . 6  class  dom  x
83, 7wfn 4587 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 360 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1537 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1532 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 178 1  wff  (CHOICE  <->  A. x E. f ( f  C_  x  /\  f  Fn  dom  x ) )
Colors of variables: wff set class
This definition is referenced by:  dfac3  7632  ac7  7984
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