Theorem syl3anl

Description: A triple syllogism inference. (Contributed by NM, 24-Dec-2006)

	Ref	Expression
Hypotheses	syl3anl.1	|- ( ph -> ps )
	syl3anl.2	|- ( ch -> th )
	syl3anl.3	|- ( ta -> et )
	syl3anl.4	|- ( ( ( ps /\ th /\ et ) /\ ze ) -> si )
Assertion	syl3anl	|- ( ( ( ph /\ ch /\ ta ) /\ ze ) -> si )

Proof

Step	Hyp	Ref	Expression
1		syl3anl.1	|- ( ph -> ps )
2		syl3anl.2	|- ( ch -> th )
3		syl3anl.3	|- ( ta -> et )
4		syl3anl.4	|- ( ( ( ps /\ th /\ et ) /\ ze ) -> si )
5	1 2 3	3anim123i	|- ( ( ph /\ ch /\ ta ) -> ( ps /\ th /\ et ) )
6	5 4	sylan	|- ( ( ( ph /\ ch /\ ta ) /\ ze ) -> si )