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Definition df-ac 8488
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 8830 as our definition, because the equivalence to more standard forms (dfac2 8502) 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 8830 itself as dfac0 8504. (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 8487 . 2  wff CHOICE
2 vf . . . . . . 7  setvar  f
32cv 1397 . . . . . 6  class  f
4 vx . . . . . . 7  setvar  x
54cv 1397 . . . . . 6  class  x
63, 5wss 3461 . . . . 5  wff  f  C_  x
75cdm 4988 . . . . . 6  class  dom  x
83, 7wfn 5565 . . . . 5  wff  f  Fn 
dom  x
96, 8wa 367 . . . 4  wff  ( f 
C_  x  /\  f  Fn  dom  x )
109, 2wex 1617 . . 3  wff  E. f
( f  C_  x  /\  f  Fn  dom  x )
1110, 4wal 1396 . 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  8493  ac7  8844
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