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Mirrors > Home > ILE Home > Th. List > ax10  Unicode version 
Description: Axiom of Quantifier
Substitution. One of the equality and substitution
axioms of predicate calculus with equality. Appears as Lemma L12 in
[Megill] p. 445 (p. 12 of the preprint).
The original version of this axiom was ax10o 1406 ("o" for "old") and was replaced with this shorter ax10 1267 in May 2008. The old axiom is proved from this one as theorem ax10o 1405. Conversely, this axiom is proved from ax10o 1406 as theorem ax10 1407. (Contributed by NM, 5Aug1993.) 
Ref  Expression 

ax10 
Step  Hyp  Ref  Expression 

1  vx  . . . 4  
2  vy  . . . 4  
3  1, 2  weq 1263  . . 3 
4  3, 1  wal 1214  . 2 
5  2, 1  weq 1263  . . 3 
6  5, 2  wal 1214  . 2 
7  4, 6  wi 4  1 
Colors of variables: wff set class 
This axiom is referenced by: alequcom 1277 ax10o 1405 
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