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Theorem syl3an2b 1384
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an2b.1 (𝜑𝜒)
syl3an2b.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an2b ((𝜓𝜑𝜃) → 𝜏)

Proof of Theorem syl3an2b
StepHypRef Expression
1 syl3an2b.1 . . 3 (𝜑𝜒)
21biimpi 208 . 2 (𝜑𝜒)
3 syl3an2b.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an2 1144 1 ((𝜓𝜑𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  w3a 1068
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 199  df-an 388  df-3an 1070
This theorem is referenced by:  omlimcl  8005  cflim2  9483  isdrngd  19250  rintopn  21221  cmpcld  21714  funvtxval0  26503  cusgr0v  26913  2clwwlk2clwwlklem  27883  cgrcomlr  32986  dissneqlem  34069  pmapglb  36357
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