Theorem 3syl

Description: Inference chaining two syllogisms syl . Inference associated with imim12i . (Contributed by NM, 28-Dec-1992)

	Ref	Expression
Hypotheses	3syl.1	|- ( ph -> ps )
	3syl.2	|- ( ps -> ch )
	3syl.3	|- ( ch -> th )
Assertion	3syl	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		3syl.1	|- ( ph -> ps )
2		3syl.2	|- ( ps -> ch )
3		3syl.3	|- ( ch -> th )
4	1 2	syl	|- ( ph -> ch )
5	4 3	syl	|- ( ph -> th )