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Theorem syl3an2br 1358
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an2br.1 (𝜒𝜑)
syl3an2br.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an2br ((𝜓𝜑𝜃) → 𝜏)

Proof of Theorem syl3an2br
StepHypRef Expression
1 syl3an2br.1 . . 3 (𝜒𝜑)
21biimpri 217 . 2 (𝜑𝜒)
3 syl3an2br.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an2 1352 1 ((𝜓𝜑𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  w3a 1031
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 196  df-an 385  df-3an 1033
This theorem is referenced by:  igenval  33030
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