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Mirrors > Home > MPE Home > Th. List > dfac  Structured version Unicode version 
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 axac 8902 as our definition, because the equivalence to more standard forms (dfac2 8574) 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 axac 8902 itself as dfac0 8576. (Contributed by Mario Carneiro, 22Feb2015.) 
Ref  Expression 

dfac  CHOICE 
Step  Hyp  Ref  Expression 

1  wac 8559  . 2 CHOICE  
2  vf  . . . . . . 7  
3  2  cv 1437  . . . . . 6 
4  vx  . . . . . . 7  
5  4  cv 1437  . . . . . 6 
6  3, 5  wss 3442  . . . . 5 
7  5  cdm 4859  . . . . . 6 
8  3, 7  wfn 5602  . . . . 5 
9  6, 8  wa 371  . . . 4 
10  9, 2  wex 1658  . . 3 
11  10, 4  wal 1436  . 2 
12  1, 11  wb 188  1 CHOICE 
Colors of variables: wff setvar class 
This definition is referenced by: dfac3 8565 ac7 8916 
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