Theorem mpbid

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	mpbid.min	$$⊢\phi \to \psi$$
	mpbid.maj	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	mpbid	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		mpbid.min	$$⊢\phi \to \psi$$
2		mpbid.maj	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
3	2	biimpd	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	1 3	mpd	$$⊢\phi \to \chi$$