Satisfiability as Non-Equivalence to Falsum (Propositional Logic)

Definition

Satisfiability as Non-Equivalence to Falsum (Propositional Logic)

A formula $P$ is satisfiable if and only if it is not equivalent to falsum $\perp$:

$$P\text{ satisfiable}⟺P\not\equiv \perp .$$

Reason

One interpretation is enough

$P\equiv \perp$ would mean $I(P)=I(\perp )$ for every interpretation $I$. If that fails, there is some $I$ with $I(P)\ne I(\perp )$; since only two truth values exist, $I(P)=I(\top )$, which is exactly satisfiability.