Theorem spcedv

Description: Existential specialization, using implicit substitution, deduction version. (Contributed by RP, 12-Aug-2020) (Revised by AV, 16-Aug-2024)

	Ref	Expression
Hypotheses	spcedv.1	|- ( ph -> X e. V )
	spcedv.2	|- ( ph -> ch )
	spcedv.3	|- ( x = X -> ( ps <-> ch ) )
Assertion	spcedv	|- ( ph -> E. x ps )

Proof

Step	Hyp	Ref	Expression
1		spcedv.1	|- ( ph -> X e. V )
2		spcedv.2	|- ( ph -> ch )
3		spcedv.3	|- ( x = X -> ( ps <-> ch ) )
4	3	spcegv	|- ( X e. V -> ( ch -> E. x ps ) )
5	1 2 4	sylc	|- ( ph -> E. x ps )