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Theorem syl3an1b 1182
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an1b.1 (𝜑𝜓)
syl3an1b.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an1b ((𝜑𝜒𝜃) → 𝜏)

Proof of Theorem syl3an1b
StepHypRef Expression
1 syl3an1b.1 . . 3 (𝜑𝜓)
21biimpi 117 . 2 (𝜑𝜓)
3 syl3an1b.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an1 1179 1 ((𝜑𝜒𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  irrmul  8679  xrlttr  8817
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