Theorem syld3an1 1228

Description: A syllogism inference. (Contributed by NM, 7-Jul-2008.)

Hypotheses

Ref	Expression
syld3an1.1	|- ((ch /\ ps /\ th) -> ph)
syld3an1.2	|- ((ph /\ ps /\ th) -> ta)

Assertion

Ref	Expression
syld3an1	|- ((ch /\ ps /\ th) -> ta)

Proof of Theorem syld3an1

Step	Hyp	Ref	Expression
1		syld3an1.1	. . . 4 |- ((ch /\ ps /\ th) -> ph)
2	1	3com13 1156	. . 3 |- ((th /\ ps /\ ch) -> ph)
3		syld3an1.2	. . . 4 |- ((ph /\ ps /\ th) -> ta)
4	3	3com13 1156	. . 3 |- ((th /\ ps /\ ph) -> ta)
5	2, 4	syld3an3 1227	. 2 |- ((th /\ ps /\ ch) -> ta)
6	5	3com13 1156	1 |- ((ch /\ ps /\ th) -> ta)

Syntax hints:   -> wi 4   /\ 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)