Theorem mtbid

Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995)

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

Proof

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