Theorem mpbiri

Description: An inference from a nested biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 25-Oct-2012)

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

Proof

Step	Hyp	Ref	Expression
1		mpbiri.min	$$⊢\chi$$
2		mpbiri.maj	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
3	1	a1i	$$⊢\phi \to \chi$$
4	3 2	mpbird	$$⊢\phi \to \psi$$