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Definition df-ac 7739
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 8081 as our definition, because the equivalence to more standard forms (dfac2 7753) 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 8081 itself as dfac0 7755. (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 7738 . 2  wff CHOICE
2 vf . . . . . . 7  set  f
32cv 1622 . . . . . 6  class  f
4 vx . . . . . . 7  set  x
54cv 1622 . . . . . 6  class  x
63, 5wss 3153 . . . . 5  wff  f  C_  x
75cdm 4688 . . . . . 6  class  dom  x
83, 7wfn 5216 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 358 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1528 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1527 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 176 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  7744  ac7  8096
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