Theorem rspc2va

Description: 2-variable restricted specialization, using implicit substitution. (Contributed by NM, 18-Jun-2014)

	Ref	Expression
Hypotheses	rspc2v.1	|- ( x = A -> ( ph <-> ch ) )
	rspc2v.2	|- ( y = B -> ( ch <-> ps ) )
Assertion	rspc2va	|- ( ( ( A e. C /\ B e. D ) /\ A. x e. C A. y e. D ph ) -> ps )

Proof

Step	Hyp	Ref	Expression
1		rspc2v.1	|- ( x = A -> ( ph <-> ch ) )
2		rspc2v.2	|- ( y = B -> ( ch <-> ps ) )
3	1 2	rspc2v	|- ( ( A e. C /\ B e. D ) -> ( A. x e. C A. y e. D ph -> ps ) )
4	3	imp	|- ( ( ( A e. C /\ B e. D ) /\ A. x e. C A. y e. D ph ) -> ps )