Axiom ax-10o 1709

Description: Axiom ax-10o 1709 ("o" for "old") was the original version of ax-10 1498, before it was discovered (in May 2008) that the shorter ax-10 1498 could replace it. It appears as Axiom scheme C11' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is redundant, as shown by Theorem ax10o 1708.

Normally, ax10o 1708 should be used rather than ax-10o 1709, except by theorems specifically studying the latter's properties. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-10o	|- ( A. x x = y -> ( A. x ph -> A. y ph ) )

Detailed syntax breakdown of Axiom ax-10o

Step	Hyp	Ref	Expression
1		vx	. . . 4 setvar x
2		vy	. . . 4 setvar y
3	1, 2	weq 1496	. . 3 wff x = y
4	3, 1	wal 1346	. 2 wff A. x x = y
5		wph	. . . 4 wff ph
6	5, 1	wal 1346	. . 3 wff A. x ph
7	5, 2	wal 1346	. . 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:  ax10  1710