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Definition df-ac 8002
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 8344 as our definition, because the equivalence to more standard forms (dfac2 8016) 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 8344 itself as dfac0 8018. (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 8001 . 2  wff CHOICE
2 vf . . . . . . 7  set  f
32cv 1652 . . . . . 6  class  f
4 vx . . . . . . 7  set  x
54cv 1652 . . . . . 6  class  x
63, 5wss 3322 . . . . 5  wff  f  C_  x
75cdm 4881 . . . . . 6  class  dom  x
83, 7wfn 5452 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 360 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1551 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1550 . 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  8007  ac7  8358
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