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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 8344 as our definition, because the equivalence to more standard forms (dfac2 8016) 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 8344 itself as dfac0 8018. (Contributed by Mario Carneiro, 22Feb2015.) 
Ref  Expression 

dfac  CHOICE 
Step  Hyp  Ref  Expression 

1  wac 8001  . 2 CHOICE  
2  vf  . . . . . . 7  
3  2  cv 1652  . . . . . 6 
4  vx  . . . . . . 7  
5  4  cv 1652  . . . . . 6 
6  3, 5  wss 3322  . . . . 5 
7  5  cdm 4881  . . . . . 6 
8  3, 7  wfn 5452  . . . . 5 
9  6, 8  wa 360  . . . 4 
10  9, 2  wex 1551  . . 3 
11  10, 4  wal 1550  . 2 
12  1, 11  wb 178  1 CHOICE 
Colors of variables: wff set class 
This definition is referenced by: dfac3 8007 ac7 8358 
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