| ⊢ | g ⊃ g1 ⇒ ⊢ f ; g ⊃ f ; g1 | RightChopImpChop | 
Proof:
| 1 | ⊢ g ⊃ g1                                       | given                      | 
| 2  | ⊢  (g  ⊃ g1)                            | |
| 3  | ⊢  (g  ⊃ g1) ⊃ (f ; g)  ⊃ (f ; g1) | |
| 4  | ⊢ f ; g ⊃ f ; g1                             | 
qed
Here is a derived rule that is a corollary of RightChopImpChop: