Theorem syl3an3b 1266

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 119	. 2 |- ( ph -> th )
3		syl3an3b.2	. 2 |- ( ( ps /\ ch /\ th ) -> ta )
4	2, 3	syl3an3 1263	1 |- ( ( ps /\ ch /\ ph ) -> ta )

Syntax hints:   -> wi 4   <-> wb 104   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  fvun2  5553  nnmsucr  6456  apreim  8501  xrlttr  9731  xrltso  9732  iccdil  9934  icccntr  9936  absexpzap  11022  unicld  12756