Equivalent Formula Laws

• Implication:
  F → G = ¬ F ∨ G
  F ↔ G = (F → G) ∧ (G → F)
  A ∧ B ∧ C → D = ¬ A ∨ ¬ B ∨ ¬ C ∨ D
  
• De Morgan's Laws:
  ¬ (F ∨ G) = ¬ F ∧ ¬ G
  ¬ (F ∧ G) = ¬ F ∨ ¬ G
  
• Distributive:
  F ∨ (G ∧ H) = (F ∨ G) ∧ (F ∨ H)
  F ∧ (G ∨ H) = (F ∧ G) ∨ (F ∧ H)

Inference Rules

• Modus Ponens: P, P → QQ or P, P → Q ⊢ Q