Axiom ax-7d 2295

Description: Distinct variable version of ax-7 1734. (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 1540	. . 3 wff ∀yφ
4		vx	. . 3 setvar x
5	3, 4	wal 1540	. 2 wff ∀x∀yφ
6	1, 4	wal 1540	. . 3 wff ∀xφ
7	6, 2	wal 1540	. 2 wff ∀y∀xφ
8	5, 7	wi 4	1 wff (∀x∀yφ → ∀y∀xφ)

This axiom is referenced by: (None)