 Lemma 7. If \(\Gamma_1\) and \(\Gamma_2\) differ only in that wherever \(\Gamma_1\) contains \(\theta\), \(\Gamma_2\) contains \(\theta(t|t')\), then for any sentence \(\phi\) not containing \(t\) or \(t'\), if \(\Gamma_1\vdash\phi\) then \(\Gamma_2\vdash\phi\). 