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Theorem sylan2i 686
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 499 1 (𝜓 → ((𝜒𝜑) → 𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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
This theorem is referenced by:  syl2ani  687  odi  7644  pssnn  8163  ltexprlem7  9849  ltaprlem  9851  sup2  10964  filufint  21705  pjnormssi  28997  poimirlem27  33407  poimirlem31  33411  pellex  37218
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