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Axiom ax-10 2140
 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 2139 ("o" for "old") and was replaced with this shorter ax-10 2140 in May 2008. The old axiom is proved from this one as theorem ax10o 1952. Conversely, this axiom is proved from ax-10o 2139 as theorem ax10from10o 2177. This axiom was proved redundant in July 2015. See theorem ax10 1944. This axiom is obsolete and should no longer be used. It is proved above as theorem ax10 1944. (Contributed by NM, 16-May-2008.) (New usage is discouraged.)
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 1643 . . 3 wff x = y
43, 1wal 1540 . 2 wff x x = y
52, 1weq 1643 . . 3 wff y = x
65, 2wal 1540 . 2 wff y y = x
74, 6wi 4 1 wff (x x = yy y = x)
 Colors of variables: wff setvar class This axiom is referenced by:  ax10o-o  2203
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