| ⊢ | f ; g ∧ f g1 ⊃ f ; (g ∧ g1) | ChopAndYieldsImp | 
This shows how yields adds information to the right of a suitable chop formula. 
Proof:
| 1 | ⊢ g ⊃ (g ∧ g1) ∨¬g1                     | |
| 2  | ⊢ f ; g ⊃ f ; (g ∧ g1) ∨ f ; ¬g1      | |
| 3  | ⊢ f ; g ∧¬(f ; ¬g1) ⊃ f ; (g ∧ g1) | |
| 4  | ⊢ f ; g ∧ f  g1 ⊃ f ; (g ∧ g1)        | 3, def. of               | 
qed
Here is a corollary: