Theorem mtbii

Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 27-Nov-1995)

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

Proof

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