Theorem mpbi

Description: An inference from a biconditional, related to modus ponens. (Contributed by NM, 11-May-1993)

	Ref	Expression
Hypotheses	mpbi.min	$$⊢\phi$$
	mpbi.maj	$$⊢\phi \leftrightarrow \psi$$
Assertion	mpbi	$$⊢\psi$$

Proof

Step	Hyp	Ref	Expression
1		mpbi.min	$$⊢\phi$$
2		mpbi.maj	$$⊢\phi \leftrightarrow \psi$$
3	2	biimpi	$$⊢\phi \to \psi$$
4	1 3	ax-mp	$$⊢\psi$$