| ⊢ | f ; g ∧ h ⊃ f ; (g ∧ h) | ChopAndBoxImport | 
Proof:
| 1 | ⊢  h ∧ f ; g ⊃ f ; (h ∧ g)  | |
| 2  | ⊢ f ; (h ∧ g) ≡ f ; (g ∧ h) | |
| 3  | ⊢  h ∧ f ; g ⊃ f ; (g ∧ h)  | 
qed
The following are easily proved:
| ⊢ | f ; (g ∧ g1) ⊃ f ; g | ChopAndA | 
| ⊢ | f ; (g ∧ g1) ⊃ f ; g1 | ChopAndB | 
| ⊢ | f ; (g ∧ g1) ≡ f ; (g1 ∧ g) | ChopAndCommute |