Theorem syl3an3b 1288

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 120	. 2 |- ( ph -> th )
3		syl3an3b.2	. 2 |- ( ( ps /\ ch /\ th ) -> ta )
4	2, 3	syl3an3 1285	1 |- ( ( ps /\ ch /\ ph ) -> ta )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  fvun2  5646  nnmsucr  6574  apreim  8676  xrlttr  9917  xrltso  9918  iccdil  10120  icccntr  10122  absexpzap  11391  unicld  14588