Axiom ax-10d 33145

Description: Distinct variable version of axc11n 2423. (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 1963	. . 3 wff 𝑥 = 𝑦
4	3, 1	wal 1536	. 2 wff ∀𝑥 𝑥 = 𝑦
5	2, 1	weq 1963	. . 3 wff 𝑦 = 𝑥
6	5, 2	wal 1536	. 2 wff ∀𝑦 𝑦 = 𝑥
7	4, 6	wi 4	1 wff (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)

This axiom is referenced by: (None)