| ⊢ w ∧ (f ⌢ g) ⊃ (w ∧ f) ⌢ g | StateAndChopImport | 
Proof:
| 1 | w  ⊃  w                        | |
| 2  | w ∧ (f ⌢ g)  ⊃  w ∧ (f ⌢ g) | |
| 3  |  w ∧ (f ⌢ g)  ⊃ (w ∧ f) ⌢ g | |
| 4  | w ∧ (f ⌢ g)  ⊃ (w ∧ f) ⌢ g  | 
qed
We can easily combine this with theorem StateChopExportA to deduce the equivalence below: