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Definition df-ac 7989
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 8331 as our definition, because the equivalence to more standard forms (dfac2 8003) 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 8331 itself as dfac0 8005. (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 7988 . 2  wff CHOICE
2 vf . . . . . . 7  set  f
32cv 1651 . . . . . 6  class  f
4 vx . . . . . . 7  set  x
54cv 1651 . . . . . 6  class  x
63, 5wss 3312 . . . . 5  wff  f  C_  x
75cdm 4870 . . . . . 6  class  dom  x
83, 7wfn 5441 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 359 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1550 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1549 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 177 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  7994  ac7  8345
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