Theorem mtbiri

Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 24-Aug-1995)

	Ref	Expression
Hypotheses	mtbiri.min	|- -. ch
	mtbiri.maj	|- ( ph -> ( ps <-> ch ) )
Assertion	mtbiri	|- ( ph -> -. ps )

Proof

Step	Hyp	Ref	Expression
1		mtbiri.min	|- -. ch
2		mtbiri.maj	|- ( ph -> ( ps <-> ch ) )
3	2	biimpd	|- ( ph -> ( ps -> ch ) )
4	1 3	mtoi	|- ( ph -> -. ps )