Axiom ax-8d 31142

Description: Distinct variable version of ax-7 1935. (Contributed by Mario Carneiro, 14-Aug-2015.)

Assertion

Ref	Expression
ax-8d	|- ( x = y -> ( x = z -> y = z ) )

Distinct variable group:   x, y, z

Detailed syntax breakdown of Axiom ax-8d

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

This axiom is referenced by: (None)