Theorem mpbii

Description: An inference from a nested biconditional, related to modus ponens. (Contributed by NM, 16-May-1993) (Proof shortened by Wolf Lammen, 25-Oct-2012)

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

Proof

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