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)