Theorem syld3an2 1229

Description: A syllogism inference. (Contributed by NM, 20-May-2007.)

Hypotheses

Ref	Expression
syld3an2.1	|- ((ph /\ ch /\ th) -> ps)
syld3an2.2	|- ((ph /\ ps /\ th) -> ta)

Assertion

Ref	Expression
syld3an2	|- ((ph /\ ch /\ th) -> ta)

Proof of Theorem syld3an2

Step	Hyp	Ref	Expression
1		syld3an2.1	. . . 4 |- ((ph /\ ch /\ th) -> ps)
2	1	3com23 1157	. . 3 |- ((ph /\ th /\ ch) -> ps)
3		syld3an2.2	. . . 4 |- ((ph /\ ps /\ th) -> ta)
4	3	3com23 1157	. . 3 |- ((ph /\ th /\ ps) -> ta)
5	2, 4	syld3an3 1227	. 2 |- ((ph /\ th /\ ch) -> ta)
6	5	3com23 1157	1 |- ((ph /\ ch /\ 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)