Theorem nsyl3

Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995)

	Ref	Expression
Hypotheses	nsyl3.1	|- ( ph -> -. ps )
	nsyl3.2	|- ( ch -> ps )
Assertion	nsyl3	|- ( ch -> -. ph )

Proof

Step	Hyp	Ref	Expression
1		nsyl3.1	|- ( ph -> -. ps )
2		nsyl3.2	|- ( ch -> ps )
3	1	a1i	|- ( ch -> ( ph -> -. ps ) )
4	2 3	mt2d	|- ( ch -> -. ph )