Users' Mathboxes Mathbox for Giovanni Mascellani < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  cnfn2dd Structured version   Visualization version   GIF version

Theorem cnfn2dd 35530
Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypotheses
Ref Expression
cnfn2dd.1 (𝜑 → (𝜓𝜃))
cnfn2dd.2 (𝜑 → (𝜓 → (𝜒 ∨ ¬ 𝜃)))
Assertion
Ref Expression
cnfn2dd (𝜑 → (𝜓𝜒))

Proof of Theorem cnfn2dd
StepHypRef Expression
1 cnfn2dd.1 . . 3 (𝜑 → (𝜓𝜃))
2 notnot 144 . . 3 (𝜃 → ¬ ¬ 𝜃)
31, 2syl6 35 . 2 (𝜑 → (𝜓 → ¬ ¬ 𝜃))
4 cnfn2dd.2 . 2 (𝜑 → (𝜓 → (𝜒 ∨ ¬ 𝜃)))
53, 4cnf2dd 35528 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:  mpobi123f  35599  mptbi12f  35603  ac6s6  35609
  Copyright terms: Public domain W3C validator