Semantic Consequence as Tautological Conditional

Theorem
Let $\mathcal F$ be a finite set of WFFs of propositional logic.

Let $\mathbf A$ be another WFF.

Then the following are equivalent:

that is, $\mathbf A$ is a semantic consequence of $\mathcal F$ iff $\displaystyle \bigwedge \mathcal F \implies \mathbf A$ is a tautology.

Here, $\displaystyle \bigwedge \mathcal F$ is the conjunction of $\mathcal F$.