Theorem mprgbir

Description: Modus ponens on biconditional combined with restricted generalization. (Contributed by NM, 21-Mar-2004)

	Ref	Expression
Hypotheses	mprgbir.1	|- ( ph <-> A. x e. A ps )
	mprgbir.2	|- ( x e. A -> ps )
Assertion	mprgbir	|- ph

Proof

Step	Hyp	Ref	Expression
1		mprgbir.1	|- ( ph <-> A. x e. A ps )
2		mprgbir.2	|- ( x e. A -> ps )
3	2	rgen	|- A. x e. A ps
4	3 1	mpbir	|- ph