Theorem syl3an3br 1269

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

Hypotheses

Ref	Expression
syl3an3br.1	|- ( th <-> ph )
syl3an3br.2	|- ( ( ps /\ ch /\ th ) -> ta )

Assertion

Ref	Expression
syl3an3br	|- ( ( ps /\ ch /\ ph ) -> ta )

Proof of Theorem syl3an3br

Step	Hyp	Ref	Expression
1		syl3an3br.1	. . 3 |- ( th <-> ph )
2	1	biimpri 132	. 2 |- ( ph -> th )
3		syl3an3br.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:  opelrng  4835  phpeqd  6894