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Mirrors > Home > ILE Home > Th. List > ax10  Structured version 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 1577 ("o" for "old") and was replaced with this shorter ax10 1369 in May 2008. The old axiom is proved from this one as theorem ax10o 1576. Conversely, this axiom is proved from ax10o 1577 as theorem ax10 1578. (Contributed by NM, 5Aug1993.) 
Ref  Expression 

ax10 
Step  Hyp  Ref  Expression 

1  vx  . . . 4  
2  vy  . . . 4  
3  1, 2  weq 1365  . . 3 
4  3, 1  wal 1221  . 2 
5  2, 1  weq 1365  . . 3 
6  5, 2  wal 1221  . 2 
7  4, 6  wi 4  1 
Colors of variables: wff set class 
This axiom is referenced by: alequcom 1381 ax10o 1576 naecoms 1585 oprabidlem 5448 
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