Theorem mpgbir

Description: Modus ponens on biconditional combined with generalization. (Contributed by NM, 24-May-1994) (Proof shortened by Stefan Allan, 28-Oct-2008)

	Ref	Expression
Hypotheses	mpgbir.1	$$⊢\phi \leftrightarrow \forall x\psi$$
	mpgbir.2	$$⊢\psi$$
Assertion	mpgbir	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		mpgbir.1	$$⊢\phi \leftrightarrow \forall x\psi$$
2		mpgbir.2	$$⊢\psi$$
3	2	ax-gen	$$⊢\forall x\psi$$
4	3 1	mpbir	$$⊢\phi$$