Axiom ax-c11 32378

Description: Axiom ax-c11 32378 was the original version of ax-c11n 32379 ("n" for "new"), before it was discovered (in May 2008) that the shorter ax-c11n 32379 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This axiom is obsolete and should no longer be used.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 2109. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-c11	|- ( A. x x = y -> ( A. x ph -> A. y ph ) )

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 1780	. . 3 wff x = y
4	3, 1	wal 1435	. 2 wff A. x x = y
5		wph	. . . 4 wff ph
6	5, 1	wal 1435	. . 3 wff A. x ph
7	5, 2	wal 1435	. . 3 wff A. y ph
8	6, 7	wi 4	. 2 wff ( A. x ph -> A. y ph )
9	4, 8	wi 4	1 wff ( A. x x = y -> ( A. x ph -> A. y ph ) )

This axiom is referenced by:  aecom-o  32390  hbae-o  32392  dral1-o  32393  axc11nfromc11  32416  dvelimf-o  32419