Theorem spvv

Description: Specialization, using implicit substitution. Version of spv with a disjoint variable condition, which does not require ax-7 , ax-12 , ax-13 . (Contributed by NM, 30-Aug-1993) (Revised by BJ, 31-May-2019)

	Ref	Expression
Hypothesis	spvv.1	|- ( x = y -> ( ph <-> ps ) )
Assertion	spvv	|- ( A. x ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		spvv.1	|- ( x = y -> ( ph <-> ps ) )
2	1	biimpd	|- ( x = y -> ( ph -> ps ) )
3	2	spimvw	|- ( A. x ph -> ps )