Theorem mpbir

Description: An inference from a biconditional, related to modus ponens. (Contributed by NM, 28-Dec-1992)

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

Proof

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