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Definition df-ac 8545
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 8887 as our definition, because the equivalence to more standard forms (dfac2 8559) 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 8887 itself as dfac0 8561. (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 8544 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1436 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1436 . . . . . 6  class  x
63, 5wss 3442 . . . . 5  wff  f  C_  x
75cdm 4854 . . . . . 6  class  dom  x
83, 7wfn 5596 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 370 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1659 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1435 . 2  wff  A. x E. f ( f  C_  x  /\  f  Fn  dom  x )
121, 11wb 187 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  8550  ac7  8901
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