Theorem nsyl2

Description: A negated syllogism inference. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 14-Nov-2023)

	Ref	Expression
Hypotheses	nsyl2.1	|- ( ph -> -. ps )
	nsyl2.2	|- ( -. ch -> ps )
Assertion	nsyl2	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		nsyl2.1	|- ( ph -> -. ps )
2		nsyl2.2	|- ( -. ch -> ps )
3	1 2	nsyl3	|- ( -. ch -> -. ph )
4	3	con4i	|- ( ph -> ch )