Satisfiable Set minus Formula is Satisfiable

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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.

$\blacksquare$


Also see


Sources