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Definition df-ac 8282
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 8624 as our definition, because the equivalence to more standard forms (dfac2 8296) 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 8624 itself as dfac0 8298. (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 8281 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1363 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1363 . . . . . 6  class  x
63, 5wss 3325 . . . . 5  wff  f  C_  x
75cdm 4836 . . . . . 6  class  dom  x
83, 7wfn 5410 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 369 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1591 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1362 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 184 1  wff  (CHOICE  <->  A. x E. f ( f  C_  x  /\  f  Fn  dom  x ) )
Colors of variables: wff setvar class
This definition is referenced by:  dfac3  8287  ac7  8638
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