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Theorem olcnd 874
 Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017.) (Proof shortened by Wolf Lammen, 13-Apr-2024.)
Hypotheses
Ref Expression
olcnd.1 (𝜑 → (𝜓𝜒))
olcnd.2 (𝜑 → ¬ 𝜒)
Assertion
Ref Expression
olcnd (𝜑𝜓)

Proof of Theorem olcnd
StepHypRef Expression
1 olcnd.2 . 2 (𝜑 → ¬ 𝜒)
2 olcnd.1 . . 3 (𝜑 → (𝜓𝜒))
32ord 861 . 2 (𝜑 → (¬ 𝜓𝜒))
41, 3mt3d 150 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844 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 210  df-or 845 This theorem is referenced by:  orcnd  876  fzone1  30553  zarclssn  31230  eulerpartlemgvv  31748  lcmineqlem23  39338  finnzfsuppd  40908
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