# Finished Branch Lemma/Corollary

## Corollary to Finished Branch Lemma

Let $\Gamma$ be a finished branch of a propositional tableau $\left({T, \mathbf H, \Phi}\right)$.

Then $\Phi \left[{\Gamma}\right]$, the image of $\Gamma$ under $\Phi$, is satisfiable for boolean interpretations.