1. ∼R v P 2. R v ∼P / R ≡ P 3. R ⊃ P 1, Material implication 4. ~P v R 2, Commutation 5. P ⊃ R 4, Material implication 6. (R ⊃ P) • (P ⊃ R) 3,5, Conjunction 7. R ≡ P 6, Material equivalence Edwin