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Axiom ax-c11n 33066
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 33065 and was replaced with this shorter ax-c11n 33066 ("n" for "new") in May 2008. The old axiom is proved from this one as theorem axc11 2206. Conversely, this axiom is proved from ax-c11 33065 as theorem axc11nfromc11 33104.

This axiom was proved redundant in July 2015. See theorem axc11n 2199.

This axiom is obsolete and should no longer be used. It is proved above as theorem axc11n 2199. (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 1824 . . 3 wff 𝑥 = 𝑦
43, 1wal 1472 . 2 wff 𝑥 𝑥 = 𝑦
52, 1weq 1824 . . 3 wff 𝑦 = 𝑥
65, 2wal 1472 . 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  33129
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