Theorem mtbi

Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994) (Proof shortened by Wolf Lammen, 25-Oct-2012)

	Ref	Expression
Hypotheses	mtbi.1	|- -. ph
	mtbi.2	|- ( ph <-> ps )
Assertion	mtbi	|- -. ps

Proof

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