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Theorem syl3an3b 1271
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an3b.1 (𝜑𝜃)
syl3an3b.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an3b ((𝜓𝜒𝜑) → 𝜏)

Proof of Theorem syl3an3b
StepHypRef Expression
1 syl3an3b.1 . . 3 (𝜑𝜃)
21biimpi 119 . 2 (𝜑𝜃)
3 syl3an3b.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an3 1268 1 ((𝜓𝜒𝜑) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  w3a 973
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 975
This theorem is referenced by:  fvun2  5563  nnmsucr  6467  apreim  8522  xrlttr  9752  xrltso  9753  iccdil  9955  icccntr  9957  absexpzap  11044  unicld  12910
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