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Axiom ax-c11n 32693
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-c11 32692 and was replaced with this shorter ax-c11n 32693 ("n" for "new") in May 2008. The old axiom is proved from this one as theorem axc11 2197. Conversely, this axiom is proved from ax-c11 32692 as theorem axc11nfromc11 32730.

This axiom was proved redundant in July 2015. See theorem axc11n 2191.

This axiom is obsolete and should no longer be used. It is proved above as theorem axc11n 2191. (Contributed by NM, 16-May-2008.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c11n (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)

Detailed syntax breakdown of Axiom ax-c11n
StepHypRef Expression
1 vx . . . 4 setvar 𝑥
2 vy . . . 4 setvar 𝑦
31, 2weq 1822 . . 3 wff 𝑥 = 𝑦
43, 1wal 1466 . 2 wff 𝑥 𝑥 = 𝑦
52, 1weq 1822 . . 3 wff 𝑦 = 𝑥
65, 2wal 1466 . 2 wff 𝑦 𝑦 = 𝑥
74, 6wi 4 1 wff (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
Colors of variables: wff setvar class
This axiom is referenced by:  axc11-o  32755
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