Axiom ax-11d 2300

Description: Distinct variable version of ax-11 1746. (Contributed by Mario Carneiro, 14-Aug-2015.)

Assertion

Ref	Expression
ax-11d	⊢ (x = y → (∀yφ → ∀x(x = y → φ)))

Distinct variable group:   x,y

Allowed substitution hints:   φ(x,y)

Detailed syntax breakdown of Axiom ax-11d

Step	Hyp	Ref	Expression
1		vx	. . 3 setvar x
2		vy	. . 3 setvar y
3	1, 2	weq 1643	. 2 wff x = y
4		wph	. . . 4 wff φ
5	4, 2	wal 1540	. . 3 wff ∀yφ
6	3, 4	wi 4	. . . 4 wff (x = y → φ)
7	6, 1	wal 1540	. . 3 wff ∀x(x = y → φ)
8	5, 7	wi 4	. 2 wff (∀yφ → ∀x(x = y → φ))
9	3, 8	wi 4	1 wff (x = y → (∀yφ → ∀x(x = y → φ)))

This axiom is referenced by: (None)