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Theorem syl3an2b 1355
 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 205 . 2 (𝜑𝜒)
3 syl3an2b.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an2 1352 1 ((𝜓𝜑𝜃) → 𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  omlimcl  7545  cflim2  8968  isdrngd  18595  rintopn  20539  cmpcld  21015  funvtxval0  25690  cgrcomlr  31275  dissneqlem  32363  pmapglb  34074  cusgr0v  40650
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