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Axiom ax-10 1393
 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 1601 ("o" for "old") and was replaced with this shorter ax-10 1393 in May 2008. The old axiom is proved from this one as theorem ax10o 1600. Conversely, this axiom is proved from ax-10o 1601 as theorem ax10 1602. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-10 (x x = yy y = x)

Detailed syntax breakdown of Axiom ax-10
StepHypRef Expression
1 vx . . . 4 setvar x
2 vy . . . 4 setvar y
31, 2weq 1389 . . 3 wff x = y
43, 1wal 1240 . 2 wff x x = y
52, 1weq 1389 . . 3 wff y = x
65, 2wal 1240 . 2 wff y y = x
74, 6wi 4 1 wff (x x = yy y = x)
 Colors of variables: wff set class This axiom is referenced by:  alequcom  1405  ax10o  1600  naecoms  1609  oprabidlem  5479
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