| ⊢ | f ⊃ g ; f, ⊢ g ⊃ more ⇒ ¬f | ChopLoop | 
Proof:
| 1 | ⊢ f ⊃ g ; f       | given                          | 
| 2  | ⊢ g ⊃more           | given                          | 
| 3  | ⊢ g ; f ⊃more ; f | |
| 4  | ⊢ f ⊃more ; f    | |
| 5  | ⊢ ¬f              | 
qed
Here is a variant of lemma MoreChopContra that is useful in proofs: