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Theorem cnf2dd 33063
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)))
32orcomdd 33061 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
41, 3cnf1dd 33062 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 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 196  df-or 384  df-an 385
This theorem is referenced by:  cnfn2dd  33065  mpt2bi123f  33141  mptbi12f  33145  ac6s6  33150
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