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Axiom ax-10 1388
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 1576 ("o" for "old") and was replaced with this shorter ax-10 1388 in May 2008. The old axiom is proved from this one as theorem ax10o 1575. Conversely, this axiom is proved from ax-10o 1576 as theorem ax10 1577.

Assertion
Ref Expression
ax-10 (x x = yy y = x)

Detailed syntax breakdown of Axiom ax-10
StepHypRef Expression
1 vx . . . 4 set x
2 vy . . . 4 set y
31, 2weq 1384 . . 3 wff x = y
43, 1wal 1335 . 2 wff x x = y
52, 1weq 1384 . . 3 wff y = x
65, 2wal 1335 . 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  1399  a9wa9lem8  1413  a9wa9lem8OLD  1414  ax10o  1575
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