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✹
5.((𝐴→𝐶)∧(𝐵→𝐶))→((𝐴∨𝐵)→𝐶)
((A→C)∧(B→C))→((A∨B)→C)
((A→C)∧(B→C))→((A∨B)→C)∨ Eliminationaxiom✹