| ⊢ | ¬(f ; g) ≡ f ¬g | NotChopEqvYieldsNot | 
Proof:
| 1 | ⊢ g ≡¬¬g               | |
| 2  | ⊢ f ; g ≡ f ; ¬¬g         | |
| 3  | ⊢ ¬(f ; g) ≡¬(f ; ¬¬g) | |
| 4  | ⊢ ¬(f ; g) ≡¬(f  g)      | def. of                   | 
qed
The following lemma TrueChopEqvDiamond is no longer needed since is now defined in terms of chop:
| ⊢ | true ; f ≡ f | TrueChopEqvDiamond |