Theorem syl3anl2 1231

Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Hypotheses

Ref	Expression
syl3anl2.1	|- (ph -> ch)
syl3anl2.2	|- (((ps /\ ch /\ th) /\ ta) -> et)

Assertion

Ref	Expression
syl3anl2	|- (((ps /\ ph /\ th) /\ ta) -> et)

Proof of Theorem syl3anl2

Step	Hyp	Ref	Expression
1		syl3anl2.1	. . 3 |- (ph -> ch)
2		syl3anl2.2	. . . 4 |- (((ps /\ ch /\ th) /\ ta) -> et)
3	2	ex 423	. . 3 |- ((ps /\ ch /\ th) -> (ta -> et))
4	1, 3	syl3an2 1216	. 2 |- ((ps /\ ph /\ th) -> (ta -> et))
5	4	imp 418	1 |- (((ps /\ ph /\ th) /\ ta) -> et)

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:  syl3anr2  1235