Axiom ax-10d 31145

Description: Distinct variable version of axc11n 2307. (Contributed by Mario Carneiro, 14-Aug-2015.)

Assertion

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

Distinct variable group:   x, y

Detailed syntax breakdown of Axiom ax-10d

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

This axiom is referenced by: (None)