Theorem syl3an

Description: A triple syllogism inference. (Contributed by NM, 13-May-2004)

	Ref	Expression
Hypotheses	syl3an.1	|- ( ph -> ps )
	syl3an.2	|- ( ch -> th )
	syl3an.3	|- ( ta -> et )
	syl3an.4	|- ( ( ps /\ th /\ et ) -> ze )
Assertion	syl3an	|- ( ( ph /\ ch /\ ta ) -> ze )

Proof

Step	Hyp	Ref	Expression
1		syl3an.1	|- ( ph -> ps )
2		syl3an.2	|- ( ch -> th )
3		syl3an.3	|- ( ta -> et )
4		syl3an.4	|- ( ( ps /\ th /\ et ) -> ze )
5	1 2 3	3anim123i	|- ( ( ph /\ ch /\ ta ) -> ( ps /\ th /\ et ) )
6	5 4	syl	|- ( ( ph /\ ch /\ ta ) -> ze )