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Theorem syl3an2b 1403
 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 206 . 2 (𝜑𝜒)
3 syl3an2b.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an2 1400 1 ((𝜓𝜑𝜃) → 𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   ∧ w3a 1054 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 385  df-3an 1056 This theorem is referenced by:  omlimcl  7703  cflim2  9123  isdrngd  18820  rintopn  20762  cmpcld  21253  funvtxval0  25942  funvtxval0OLD  25943  cusgr0v  26380  cgrcomlr  32230  dissneqlem  33317  pmapglb  35374
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