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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 8837 as our definition, because the equivalence to more standard forms (dfac2 8509) 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 8837 itself as dfac0 8511. (Contributed by Mario Carneiro, 22Feb2015.) 
Ref  Expression 

dfac  CHOICE 
Step  Hyp  Ref  Expression 

1  wac 8494  . 2 CHOICE  
2  vf  . . . . . . 7  
3  2  cv 1380  . . . . . 6 
4  vx  . . . . . . 7  
5  4  cv 1380  . . . . . 6 
6  3, 5  wss 3458  . . . . 5 
7  5  cdm 4985  . . . . . 6 
8  3, 7  wfn 5569  . . . . 5 
9  6, 8  wa 369  . . . 4 
10  9, 2  wex 1597  . . 3 
11  10, 4  wal 1379  . 2 
12  1, 11  wb 184  1 CHOICE 
Colors of variables: wff setvar class 
This definition is referenced by: dfac3 8500 ac7 8851 
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