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

Theorem unitresl 32837
Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Hypotheses
Ref Expression
unitresl.1 (𝜑 → (𝜓𝜒))
unitresl.2 (𝜑 → ¬ 𝜒)
Assertion
Ref Expression
unitresl (𝜑𝜓)

Proof of Theorem unitresl
StepHypRef Expression
1 unitresl.1 . 2 (𝜑 → (𝜓𝜒))
2 unitresl.2 . 2 (𝜑 → ¬ 𝜒)
3 orcom 400 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
4 df-or 383 . . 3 ((𝜒𝜓) ↔ (¬ 𝜒𝜓))
53, 4sylbb 207 . 2 ((𝜓𝜒) → (¬ 𝜒𝜓))
61, 2, 5sylc 62 1 (𝜑𝜓)
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
This theorem is referenced by:  unitresr  32838
  Copyright terms: Public domain W3C validator