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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 1582 ("o" for "old") and was replaced with this shorter ax10 1373 in May 2008. The old axiom is proved from this one as theorem ax10o 1581. Conversely, this axiom is proved from ax10o 1582 as theorem ax10 1583. (Contributed by NM, 5Aug1993.) 
Ref  Expression 

ax10 
Step  Hyp  Ref  Expression 

1  vx  . . . 4  
2  vy  . . . 4  
3  1, 2  weq 1369  . . 3 
4  3, 1  wal 1224  . 2 
5  2, 1  weq 1369  . . 3 
6  5, 2  wal 1224  . 2 
7  4, 6  wi 4  1 
Colors of variables: wff set class 
This axiom is referenced by: alequcom 1385 ax10o 1581 naecoms 1590 oprabidlem 5456 
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