Theorem syl3an3b 1220

Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Hypotheses

Ref	Expression
syl3an3b.1	|- (ph <-> th)
syl3an3b.2	|- ((ps /\ ch /\ th) -> ta)

Assertion

Ref	Expression
syl3an3b	|- ((ps /\ ch /\ ph) -> ta)

Proof of Theorem syl3an3b

Step	Hyp	Ref	Expression
1		syl3an3b.1	. . 3 |- (ph <-> th)
2	1	biimpi 186	. 2 |- (ph -> th)
3		syl3an3b.2	. 2 |- ((ps /\ ch /\ th) -> ta)
4	2, 3	syl3an3 1217	1 |- ((ps /\ ch /\ ph) -> ta)

Syntax hints:   -> wi 4   <-> wb 176   /\ 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:  nnadjoin  4521  fvun2  5381