How can a set tautologically imply every wff? Let Σ be a subset of Wp such that for some wff a, Σ |= a and Σ |= ¬a. How do I prove that Σ |= b for all b in Wp? I understand that a and ¬a will be satisfied when Σ is ...--prophetes.ai

How can a set tautologically imply every wff? Let Σ be a subset of Wp such that for some wff a, Σ |= a and Σ |= ¬a. How do I prove that Σ |= b for all b in Wp? I understand that a and ¬a will be satisfied when Σ is satisfied but I'm not sure how to go from there.

From comments by user Mauro ALLEGRANZA:

> If $\Sigma \models A$ and $\Sigma \models \
eg A$, this means that there is **no** valuation that satisfy $\Sigma$.
>
> Apply this to show $\Sigma \models B$ by contradiction.