Theorem rspcdvinvd

Description: If something is true for all then it's true for some class. (Contributed by Stanislas Polu, 9-Mar-2020)

	Ref	Expression
Hypotheses	rspcdvinvd.1	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
	rspcdvinvd.2	|- ( ph -> A e. B )
	rspcdvinvd.3	|- ( ph -> A. x e. B ps )
Assertion	rspcdvinvd	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		rspcdvinvd.1	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
2		rspcdvinvd.2	|- ( ph -> A e. B )
3		rspcdvinvd.3	|- ( ph -> A. x e. B ps )
4	2 1	rspcdv	|- ( ph -> ( A. x e. B ps -> ch ) )
5	3 4	mpd	|- ( ph -> ch )