Theorem syl3an2br 1137

Description: A syllogism inference.

Hypotheses

Ref	Expression
syl3an.1	|- ((ph /\ ps /\ ch) -> th)
syl3an2br.2	|- (ps <-> ta)

Assertion

Ref	Expression
syl3an2br	|- ((ph /\ ta /\ ch) -> th)

Proof of Theorem syl3an2br

Step	Hyp	Ref	Expression
1		syl3an.1	. 2 |- ((ph /\ ps /\ ch) -> th)
2		syl3an2br.2	. . 3 |- (ps <-> ta)
3	2	biimpri 169	. 2 |- (ta -> ps)
4	1, 3	syl3an2 1131	1 |- ((ph /\ ta /\ ch) -> th)

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

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

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