Theorem mtbird

Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 10-May-1994)

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

Proof

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