Axiom ax-c11 33190

Description: Axiom ax-c11 33190 was the original version of ax-c11n 33191 ("n" for "new"), before it was discovered (in May 2008) that the shorter ax-c11n 33191 could replace it. It appears as Axiom scheme C11' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is obsolete and should no longer be used. It is proved above as theorem axc11 2302. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-c11	⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))

Detailed syntax breakdown of Axiom ax-c11

Step	Hyp	Ref	Expression
1		vx	. . . 4 setvar 𝑥
2		vy	. . . 4 setvar 𝑦
3	1, 2	weq 1861	. . 3 wff 𝑥 = 𝑦
4	3, 1	wal 1473	. 2 wff ∀𝑥 𝑥 = 𝑦
5		wph	. . . 4 wff 𝜑
6	5, 1	wal 1473	. . 3 wff ∀𝑥𝜑
7	5, 2	wal 1473	. . 3 wff ∀𝑦𝜑
8	6, 7	wi 4	. 2 wff (∀𝑥𝜑 → ∀𝑦𝜑)
9	4, 8	wi 4	1 wff (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))

This axiom is referenced by:  aecom-o  33204  hbae-o  33206  dral1-o  33207  axc11nfromc11  33229  dvelimf-o  33232