Theorem mpbird

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 5-Aug-1993)

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

Proof

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