p → (q → r) ⊢ (p → q) → (p → r) ≡ ¬p ∨ (¬q ∨ r) ⊢ ¬(¬p ∨ q) ∨ (¬p ∨ r) (1) from (Ax) follows: q ⊢ ¬p ∨ r, q (2) from (2) and (¬L) follows: q, ¬q ⊢ ¬p ∨ r (3) from (Ax) follows: q, r ⊢ ¬p, r (4) from (3) and (∨R) follows: q, r ⊢ ¬p ∨ r (5) from (2) and (4) and (∨L) follows: q, ¬q ∨ r ⊢ ¬p ∨ r (6) from (Ax) follows: q, ¬p ⊢ ¬p, r (7) from (6) and (∨R) follows: q, ¬p ⊢ ¬p ∨ r (8) from (5) and (7) and (∨L) follows: ¬p ∨ (¬q ∨ r), q ⊢ ¬p ∨ r (9) from (Ax) follows: ¬p ∨ (¬q ∨ r), ¬p ⊢ ¬p, r (10) from (9) and (∨R) follows: ¬p ∨ (¬q ∨ r), ¬p ⊢ ¬p ∨ r (11) from (8) and (10) and (∨L) follows: ¬p ∨ (¬q ∨ r), ¬p ∨ q ⊢ ¬p ∨ r (12) from (11) and (¬R) follows: ¬p ∨ (¬q ∨ r) ⊢ ¬(¬p ∨ q), ¬p ∨ r (13) from (12) and (∨R) follows: ¬p ∨ (¬q ∨ r) ⊢ ¬(¬p ∨ q) ∨ (¬p ∨ r) QED.
https://social.lizzy.rs/system/media_attachments/files/112/514/460/209/604/856/original/ff109734fb816a17.png
*(*(void **(*)()) lizzy)() :v_trans: :v_bi:
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