Axiom ax-c10 34171

Description: A variant of ax6 2251. Axiom scheme C10' 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This axiom is obsolete and should no longer be used.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 axc10 2252. (Contributed by NM, 10-Jan-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-c10	|- ( A. x ( x = y -> A. x ph ) -> ph )

Detailed syntax breakdown of Axiom ax-c10

Step	Hyp	Ref	Expression
1		vx	. . . . 5 setvar x
2		vy	. . . . 5 setvar y
3	1, 2	weq 1874	. . . 4 wff x = y
4		wph	. . . . 5 wff ph
5	4, 1	wal 1481	. . . 4 wff A. x ph
6	3, 5	wi 4	. . 3 wff ( x = y -> A. x ph )
7	6, 1	wal 1481	. 2 wff A. x ( x = y -> A. x ph )
8	7, 4	wi 4	1 wff ( A. x ( x = y -> A. x ph ) -> ph )

This axiom is referenced by:  ax6fromc10  34181  equid1  34184  equid1ALT  34210