Axiom ax-c11n 36464

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 36463 and was replaced with this shorter ax-c11n 36464 ("n" for "new") in May 2008. The old axiom is proved from this one as Theorem axc11 2441. Conversely, this axiom is proved from ax-c11 36463 as Theorem axc11nfromc11 36502.

This axiom was proved redundant in July 2015. See Theorem axc11n 2437.

This axiom is obsolete and should no longer be used. It is proved above as Theorem axc11n 2437. (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

Step	Hyp	Ref	Expression
1		vx	. . . 4 setvar 𝑥
2		vy	. . . 4 setvar 𝑦
3	1, 2	weq 1964	. . 3 wff 𝑥 = 𝑦
4	3, 1	wal 1536	. 2 wff ∀𝑥 𝑥 = 𝑦
5	2, 1	weq 1964	. . 3 wff 𝑦 = 𝑥
6	5, 2	wal 1536	. 2 wff ∀𝑦 𝑦 = 𝑥
7	4, 6	wi 4	1 wff (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)

This axiom is referenced by:  axc11-o  36527