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Axiom ax-10 1369
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 ax-10o 1577 ("o" for "old") and was replaced with this shorter ax-10 1369 in May 2008. The old axiom is proved from this one as theorem ax10o 1576. Conversely, this axiom is proved from ax-10o 1577 as theorem ax10 1578. (Contributed by NM, 5-Aug-1993.)

Assertion
Ref Expression
ax-10

Detailed syntax breakdown of Axiom ax-10
StepHypRef Expression
1 vx . . . 4  setvar
2 vy . . . 4  setvar
31, 2weq 1365 . . 3
43, 1wal 1221 . 2
52, 1weq 1365 . . 3
65, 2wal 1221 . 2
74, 6wi 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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