Axiom ax-7d 32834

Description: Distinct variable version of ax-11 2158. (Contributed by Mario Carneiro, 14-Aug-2015.)

Assertion

Ref	Expression
ax-7d	⊢ (∀𝑥∀𝑦𝜑 → ∀𝑦∀𝑥𝜑)

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥,𝑦)

Detailed syntax breakdown of Axiom ax-7d

Step	Hyp	Ref	Expression
1		wph	. . . 4 wff 𝜑
2		vy	. . . 4 setvar 𝑦
3	1, 2	wal 1541	. . 3 wff ∀𝑦𝜑
4		vx	. . 3 setvar 𝑥
5	3, 4	wal 1541	. 2 wff ∀𝑥∀𝑦𝜑
6	1, 4	wal 1541	. . 3 wff ∀𝑥𝜑
7	6, 2	wal 1541	. 2 wff ∀𝑦∀𝑥𝜑
8	5, 7	wi 4	1 wff (∀𝑥∀𝑦𝜑 → ∀𝑦∀𝑥𝜑)

This axiom is referenced by: (None)