Theorem syl3anl1 1230

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

Hypotheses

Ref	Expression
syl3anl1.1	|- (ph -> ps)
syl3anl1.2	|- (((ps /\ ch /\ th) /\ ta) -> et)

Assertion

Ref	Expression
syl3anl1	|- (((ph /\ ch /\ th) /\ ta) -> et)

Proof of Theorem syl3anl1

Step	Hyp	Ref	Expression
1		syl3anl1.1	. . 3 |- (ph -> ps)
2	1	3anim1i 1138	. 2 |- ((ph /\ ch /\ th) -> (ps /\ ch /\ th))
3		syl3anl1.2	. 2 |- (((ps /\ ch /\ th) /\ ta) -> et)
4	2, 3	sylan 457	1 |- (((ph /\ ch /\ 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)