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Theorem syl3an3br 1365
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an3br.1 (𝜃𝜑)
syl3an3br.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an3br ((𝜓𝜒𝜑) → 𝜏)

Proof of Theorem syl3an3br
StepHypRef Expression
1 syl3an3br.1 . . 3 (𝜃𝜑)
21biimpri 218 . 2 (𝜑𝜃)
3 syl3an3br.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an3 1359 1 ((𝜓𝜒𝜑) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w3a 1036
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 197  df-an 386  df-3an 1038
This theorem is referenced by:  ordintdif  5762  lsslinds  20151  2ndcdisj2  21241  isosctrlem2  24530  endofsegid  32167
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