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Theorem syl3an1b 1359
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 206 . 2 (𝜑𝜓)
3 syl3an1b.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an1 1356 1 ((𝜑𝜒𝜃) → 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:  ovmpt2elrn  7186  irrmul  11757  xrlttr  11917  flfneii  21706  padct  29337  crefdf  29694  divrngcl  33385
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