1. (P ∧ Q) ∨ (P ∧ R)
  2. P ∧ Q - supp
  3. P - ∧E
  4. P ∧ R - supp
  5. P - ∧ E
  6. P
  7. P ∧ Q - supp
  8. Q - ∧ E
  9. Q ∨ R - ∨I
  10. P ∧ R - supp
  11. R - ∧ E
  12. R ∨ Q - ∨ I
  13. Q ∨ R
  14. P ∧ (Q ∨ R)

Chapter 23 - PL proofs theorems
theorem - ⊨ for syntax