Theorem nsyli

Description: A negated syllogism inference. (Contributed by NM, 3-May-1994)

	Ref	Expression
Hypotheses	nsyli.1	|- ( ph -> ( ps -> ch ) )
	nsyli.2	|- ( th -> -. ch )
Assertion	nsyli	|- ( ph -> ( th -> -. ps ) )

Proof

Step	Hyp	Ref	Expression
1		nsyli.1	|- ( ph -> ( ps -> ch ) )
2		nsyli.2	|- ( th -> -. ch )
3	1	con3d	|- ( ph -> ( -. ch -> -. ps ) )
4	2 3	syl5	|- ( ph -> ( th -> -. ps ) )