Satisfiable Set minus Formula is Satisfiable

Theorem
Let $\LL$ be a logical language.

Let $\mathscr M$ be a formal semantics for $\LL$.

Let $\FF$ be an $\mathscr M$-satisfiable set of formulas from $\LL$.

Let $\phi \in \FF$.

Then $\FF \setminus \set \phi$ is also $\mathscr M$-satisfiable.

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

Also see

 * Subset of Satisfiable Set is Satisfiable