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Theorem syl3an1br 1398
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an1br.1 (𝜓𝜑)
syl3an1br.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an1br ((𝜑𝜒𝜃) → 𝜏)

Proof of Theorem syl3an1br
StepHypRef Expression
1 syl3an1br.1 . . 3 (𝜓𝜑)
21biimpri 229 . 2 (𝜑𝜓)
3 syl3an1br.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an1 1155 1 ((𝜑𝜒𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  cdleme0moN  37241
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