Theorem syl3anr2 1235

Description: A syllogism inference. (Contributed by NM, 1-Aug-2007.)

Hypotheses

Ref	Expression
syl3anr2.1	|- (ph -> th)
syl3anr2.2	|- ((ch /\ (ps /\ th /\ ta)) -> et)

Assertion

Ref	Expression
syl3anr2	|- ((ch /\ (ps /\ ph /\ ta)) -> et)

Proof of Theorem syl3anr2

Step	Hyp	Ref	Expression
1		syl3anr2.1	. . 3 |- (ph -> th)
2		syl3anr2.2	. . . 4 |- ((ch /\ (ps /\ th /\ ta)) -> et)
3	2	ancoms 439	. . 3 |- (((ps /\ th /\ ta) /\ ch) -> et)
4	1, 3	syl3anl2 1231	. 2 |- (((ps /\ ph /\ ta) /\ ch) -> et)
5	4	ancoms 439	1 |- ((ch /\ (ps /\ ph /\ 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: (None)