Axiom ax-11d 31146

Description: Distinct variable version of ax-12 2047. (Contributed by Mario Carneiro, 14-Aug-2015.)

Assertion

Ref	Expression
ax-11d	|- ( x = y -> ( A. y ph -> A. x ( x = y -> ph ) ) )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Detailed syntax breakdown of Axiom ax-11d

Step	Hyp	Ref	Expression
1		vx	. . 3 setvar x
2		vy	. . 3 setvar y
3	1, 2	weq 1874	. 2 wff x = y
4		wph	. . . 4 wff ph
5	4, 2	wal 1481	. . 3 wff A. y ph
6	3, 4	wi 4	. . . 4 wff ( x = y -> ph )
7	6, 1	wal 1481	. . 3 wff A. x ( x = y -> ph )
8	5, 7	wi 4	. 2 wff ( A. y ph -> A. x ( x = y -> ph ) )
9	3, 8	wi 4	1 wff ( x = y -> ( A. y ph -> A. x ( x = y -> ph ) ) )

This axiom is referenced by: (None)