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Theorem cnfn1dd 32860
Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypotheses
Ref Expression
cnfn1dd.1 (𝜑 → (𝜓𝜒))
cnfn1dd.2 (𝜑 → (𝜓 → (¬ 𝜒𝜃)))
Assertion
Ref Expression
cnfn1dd (𝜑 → (𝜓𝜃))

Proof of Theorem cnfn1dd
StepHypRef Expression
1 cnfn1dd.1 . . 3 (𝜑 → (𝜓𝜒))
2 notnot 134 . . 3 (𝜒 → ¬ ¬ 𝜒)
31, 2syl6 34 . 2 (𝜑 → (𝜓 → ¬ ¬ 𝜒))
4 cnfn1dd.2 . 2 (𝜑 → (𝜓 → (¬ 𝜒𝜃)))
53, 4cnf1dd 32858 1 (𝜑 → (𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 381
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 195  df-or 383  df-an 384
This theorem is referenced by:  mpt2bi123f  32937  mptbi12f  32941  ac6s6  32946
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