Theorem syl3an3br 627

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	biimpr 134	. 2 |- (ta -> ch)
4	1, 3	syl3an3 621	1 |- ((ph /\ ps /\ ta ) -> th)

Syntax hints:   -> wi 2   <-> wb 127   /\ w3a 581

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

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

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