# Satisfiable Set minus Formula is Satisfiable

## Theorem

Let $\mathcal L$ be a logical language.

Let $\mathscr M$ be a formal semantics for $\mathcal L$.

Let $\mathcal F$ be an $\mathscr M$-satisfiable set of formulas from $\mathcal L$.

Let $\phi \in \mathcal F$.

Then $\mathcal F \setminus \left\{{\phi}\right\}$ is also $\mathscr M$-satisfiable.

## Proof

This is an immediate consequence of Subset of Satisfiable Set is Satisfiable.

$\blacksquare$