Theorem syl3anr3 1236

Description: A syllogism inference. (Contributed by NM, 23-Aug-2007.)

Hypotheses

Ref	Expression
syl3anr3.1	|- (ph -> ta)
syl3anr3.2	|- ((ch /\ (ps /\ th /\ ta)) -> et)

Assertion

Ref	Expression
syl3anr3	|- ((ch /\ (ps /\ th /\ ph)) -> et)

Proof of Theorem syl3anr3

Step	Hyp	Ref	Expression
1		syl3anr3.1	. . 3 |- (ph -> ta)
2	1	3anim3i 1139	. 2 |- ((ps /\ th /\ ph) -> (ps /\ th /\ ta))
3		syl3anr3.2	. 2 |- ((ch /\ (ps /\ th /\ ta)) -> et)
4	2, 3	sylan2 460	1 |- ((ch /\ (ps /\ th /\ ph)) -> 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)