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	|- -. ps
	mtbir.2	|- ( ph <-> ps )
Assertion	mtbir	|- -. ph

Proof

Step	Hyp	Ref	Expression
1		mtbir.1	|- -. ps
2		mtbir.2	|- ( ph <-> ps )
3	2	bicomi	|- ( ps <-> ph )
4	1 3	mtbi	|- -. ph