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Definition df-ac 7745
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 8087 as our definition, because the equivalence to more standard forms (dfac2 7759) 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 8087 itself as dfac0 7761. (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 7744 . 2  wff CHOICE
2 vf . . . . . . 7  set  f
32cv 1624 . . . . . 6  class  f
4 vx . . . . . . 7  set  x
54cv 1624 . . . . . 6  class  x
63, 5wss 3154 . . . . 5  wff  f  C_  x
75cdm 4691 . . . . . 6  class  dom  x
83, 7wfn 5252 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 358 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1530 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1529 . 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  7750  ac7  8102
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