Theorem syl3an3br 1138

Description: A syllogism inference.

Hypotheses

Ref	Expression
syl3an.1	|- ((ph /\ ps /\ ch) -> th)
syl3an3br.2	|- (ch <-> ta)

Assertion

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

Proof of Theorem syl3an3br

Step	Hyp	Ref	Expression
1		syl3an.1	. 2 |- ((ph /\ ps /\ ch) -> th)
2		syl3an3br.2	. . 3 |- (ch <-> ta)
3	2	biimpri 169	. 2 |- (ta -> ch)
4	1, 3	syl3an3 1132	1 |- ((ph /\ ps /\ ta) -> th)

Syntax hints:   -> wi 3   <-> wb 163   /\ w3a 858

This theorem is referenced by:  isummulc1 8473  bnj1031 13383  iserzmulc1b 14528  ordintdif 16440

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-3an 860

Copyright terms: Public domain