Axiom ax-10d 2299

Description: Distinct variable version of ax10 1944. (Contributed by Mario Carneiro, 14-Aug-2015.)

Assertion

Ref	Expression
ax-10d	⊢ (∀x x = y → ∀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 1643	. . 3 wff x = y
4	3, 1	wal 1540	. 2 wff ∀x x = y
5	2, 1	weq 1643	. . 3 wff y = x
6	5, 2	wal 1540	. 2 wff ∀y y = x
7	4, 6	wi 4	1 wff (∀x x = y → ∀y y = x)

This axiom is referenced by: (None)