Theorem syl3anr1 1234

Description: A syllogism inference. (Contributed by NM, 31-Jul-2007.)

Hypotheses

Ref	Expression
syl3anr1.1	|- (ph -> ps)
syl3anr1.2	|- ((ch /\ (ps /\ th /\ ta)) -> et)

Assertion

Ref	Expression
syl3anr1	|- ((ch /\ (ph /\ th /\ ta)) -> et)

Proof of Theorem syl3anr1

Step	Hyp	Ref	Expression
1		syl3anr1.1	. . 3 |- (ph -> ps)
2	1	3anim1i 1138	. 2 |- ((ph /\ th /\ ta) -> (ps /\ th /\ ta))
3		syl3anr1.2	. 2 |- ((ch /\ (ps /\ th /\ ta)) -> et)
4	2, 3	sylan2 460	1 |- ((ch /\ (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: (None)