We are attempting to show that there are not too many proofs under the Sheffer's stroke tableau system. We will demonstrate that an arbitrary stroke tableau proof can be simulated by a tableau proof. First, we show that an arbitrary stroke formula is equivalent to a standard formula. Proof by induction over the structure of . Base case is of the form .
Inductive case is of the form .
Therefore, for any arbitrary tableau proof using the stroke, the proof can be simulated by a tableau using , and . Therefore, there are no more stroke tableau proofs than standard tableau proofs. Therefore, stroke tableau is a consistent proof method. Case 2 is of the form . Case 4 is of the form .