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Definition df-ac 8291
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 8633 as our definition, because the equivalence to more standard forms (dfac2 8305) 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 8633 itself as dfac0 8307. (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 8290 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1368 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1368 . . . . . 6  class  x
63, 5wss 3333 . . . . 5  wff  f  C_  x
75cdm 4845 . . . . . 6  class  dom  x
83, 7wfn 5418 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 369 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1586 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1367 . 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  8296  ac7  8647
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