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Axiom ax-c11n 34646
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 34645 and was replaced with this shorter ax-c11n 34646 ("n" for "new") in May 2008. The old axiom is proved from this one as theorem axc11 2444. Conversely, this axiom is proved from ax-c11 34645 as theorem axc11nfromc11 34684.

This axiom was proved redundant in July 2015. See theorem axc11n 2439.

This axiom is obsolete and should no longer be used. It is proved above as theorem axc11n 2439. (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 2028 . . 3 wff 𝑥 = 𝑦
43, 1wal 1618 . 2 wff 𝑥 𝑥 = 𝑦
52, 1weq 2028 . . 3 wff 𝑦 = 𝑥
65, 2wal 1618 . 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  34709
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