Theorem speivw

Description: Version of spei with a disjoint variable condition, which does not require ax-13 (neither ax-7 nor ax-12 ). (Contributed by BJ, 31-May-2019)

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

Proof

Step	Hyp	Ref	Expression
1		speivw.1	|- ( x = y -> ( ph <-> ps ) )
2		speivw.2	|- ps
3	1	biimprd	|- ( x = y -> ( ps -> ph ) )
4	3 2	speiv	|- E. x ph