Axiom ax-c11 38359

Description: Axiom ax-c11 38359 was the original version of ax-c11n 38360 ("n" for "new"), before it was discovered (in May 2008) that the shorter ax-c11n 38360 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This axiom is obsolete and should no longer be used.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 2425. (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 1959	. . 3 wff 𝑥 = 𝑦
4	3, 1	wal 1532	. 2 wff ∀𝑥 𝑥 = 𝑦
5		wph	. . . 4 wff 𝜑
6	5, 1	wal 1532	. . 3 wff ∀𝑥𝜑
7	5, 2	wal 1532	. . 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  38373  hbae-o  38375  dral1-o  38376  axc11nfromc11  38398  dvelimf-o  38401