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Theorem sylan2i 593
 Description: A syllogism inference. (Contributed by NM, 1-Aug-1994.)
Hypotheses
Ref Expression
sylan2i.1 (𝜑𝜃)
sylan2i.2 (𝜓 → ((𝜒𝜃) → 𝜏))
Assertion
Ref Expression
sylan2i (𝜓 → ((𝜒𝜑) → 𝜏))

Proof of Theorem sylan2i
StepHypRef Expression
1 sylan2i.1 . . 3 (𝜑𝜃)
21a1i 11 . 2 (𝜓 → (𝜑𝜃))
3 sylan2i.2 . 2 (𝜓 → ((𝜒𝜃) → 𝜏))
42, 3sylan2d 592 1 (𝜓 → ((𝜒𝜑) → 𝜏))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 382 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 383 This theorem is referenced by:  syl2ani  594  odi  7813  pssnn  8334  ltexprlem7  10066  ltaprlem  10068  sup2  11181  filufint  21944  pjnormssi  29367  poimirlem27  33769  poimirlem31  33773  pellex  37925
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