| ⊢ finite ⊃ (f ≡ g) ⇒ ⊢ f ≡ g | FiniteImpBfEqvBfRule | 
Proof:
| 1 | finite  ⊃ (f ≡ g)   | Assump                             | 
| 2  | finite  ⊃ (f  ⊃ g) | |
| 3  |  f  ⊃  g           | |
| 4  | finite  ⊃ (g  ⊃ f) | |
| 5  |  g  ⊃  f           | |
| 6  |  f ≡ g            | 
qed
The next theorem’s proof involves the application of the previous derived inference rule together with completeness for PITL with just finite time: