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Theorem cnf2dd 35528
Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypotheses
Ref Expression
cnf2dd.1 (𝜑 → (𝜓 → ¬ 𝜃))
cnf2dd.2 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
cnf2dd (𝜑 → (𝜓𝜒))

Proof of Theorem cnf2dd
StepHypRef Expression
1 cnf2dd.1 . 2 (𝜑 → (𝜓 → ¬ 𝜃))
2 cnf2dd.2 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
3 pm1.4 866 . . 3 ((𝜒𝜃) → (𝜃𝜒))
42, 3syl6 35 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
51, 4cnf1dd 35527 1 (𝜑 → (𝜓𝜒))
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-an 400  df-or 845
This theorem is referenced by:  cnfn2dd  35530  mpobi123f  35599  mptbi12f  35603  ac6s6  35609
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