Theorem mtbir

Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994) (Proof shortened by Wolf Lammen, 14-Oct-2012)

	Ref	Expression
Hypotheses	mtbir.1	$$⊢\neg \psi$$
	mtbir.2	$$⊢\phi \leftrightarrow \psi$$
Assertion	mtbir	$$⊢\neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		mtbir.1	$$⊢\neg \psi$$
2		mtbir.2	$$⊢\phi \leftrightarrow \psi$$
3	2	bicomi	$$⊢\psi \leftrightarrow \phi$$
4	1 3	mtbi	$$⊢\neg \phi$$