Theorem syl3anl 1233

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

Hypotheses

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

Assertion

Ref	Expression
syl3anl	|- (((ph /\ ch /\ ta) /\ ze) -> si)

Proof of Theorem syl3anl

Step	Hyp	Ref	Expression
1		syl3anl.1	. . 3 |- (ph -> ps)
2		syl3anl.2	. . 3 |- (ch -> th)
3		syl3anl.3	. . 3 |- (ta -> et)
4	1, 2, 3	3anim123i 1137	. 2 |- ((ph /\ ch /\ ta) -> (ps /\ th /\ et))
5		syl3anl.4	. 2 |- (((ps /\ th /\ et) /\ ze) -> si)
6	4, 5	sylan 457	1 |- (((ph /\ ch /\ ta) /\ ze) -> si)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by: (None)