Theorem equsalhw

Description: Version of equsalh with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 29-Nov-2015) (Proof shortened by Wolf Lammen, 8-Jul-2022)

	Ref	Expression
Hypotheses	equsalhw.1	|- ( ps -> A. x ps )
	equsalhw.2	|- ( x = y -> ( ph <-> ps ) )
Assertion	equsalhw	|- ( A. x ( x = y -> ph ) <-> ps )

Proof

Step	Hyp	Ref	Expression
1		equsalhw.1	|- ( ps -> A. x ps )
2		equsalhw.2	|- ( x = y -> ( ph <-> ps ) )
3	1	nf5i	|- F/ x ps
4	3 2	equsalv	|- ( A. x ( x = y -> ph ) <-> ps )