1.𝐴→𝐴
A→A
A→Aidentityaxiom▲ Logic N⁎
2.𝐴→(𝐴∨𝐵) | 𝐵→(𝐴∨𝐵)
A→(A∨B) | B→(A∨B)
A→(A∨B) | B→(A∨B)∨ Introductionaxiom▲ Logic N⁎
3.(𝐴∧𝐵)→𝐴 | (𝐴∧𝐵)→𝐵
(A∧B)→A | (A∧B)→B
(A∧B)→A | (A∧B)→B∧ Eliminationaxiom▲ Logic N⁎
4.((𝐴→𝐵)∧(𝐴→𝐶))→(𝐴→(𝐵∧𝐶))
((A→B)∧(A→C))→(A→(B∧C))
((A→B)∧(A→C))→(A→(B∧C))∧ Introductionaxiom▲ Logic B
5.((𝐴→𝐶)∧(𝐵→𝐶))→((𝐴∨𝐵)→𝐶)
((A→C)∧(B→C))→((A∨B)→C)
((A→C)∧(B→C))→((A∨B)→C)∨ Eliminationaxiom▲ Logic B
6.𝐴→((𝐴→𝐵)→𝐵)
A→((A→B)→B)
A→((A→B)→B)Assertionaxiom✹
7.(𝐴→(𝐴→𝐵)) → (𝐴→𝐵)
(A→(A→B)) → (A→B)
(A→(A→B)) → (A→B)Contractionaxiom✹
8.𝐴→𝐵 → (𝐵→𝐶)→(𝐴→𝐶)
A→B → (B→C)→(A→C)
A→B → (B→C)→(A→C)Suffixingaxiom✹
9.𝐵→𝐶 → ((𝐴→𝐵)→(𝐴→𝐶))
B→C → ((A→B)→(A→C))
B→C → ((A→B)→(A→C))Prefixingaxiom✹
10.(𝐴→(𝐵→𝐶)) → (𝐵→(𝐴→𝐶))
(A→(B→C)) → (B→(A→C))
(A→(B→C)) → (B→(A→C))Permutationaxiom✹