Theorem mtbiri

Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 24-Aug-1995)

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

Proof

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