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Brandon Rozek 2024-10-27 17:46:45 -04:00
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@ -38,7 +38,7 @@ $$
(\forall x \phi) \implies \psi &\iff \neg (\forall x \phi) \vee \psi \tag{0.1} \\\\ (\forall x \phi) \implies \psi &\iff \neg (\forall x \phi) \vee \psi \tag{0.1} \\\\
&\iff (\exists x \neg \phi) \vee \psi \tag{2.2}\\\\ &\iff (\exists x \neg \phi) \vee \psi \tag{2.2}\\\\
&\iff \exists x (\neg \phi \vee \psi) \tag{2.1}\\\\ &\iff \exists x (\neg \phi \vee \psi) \tag{2.1}\\\\
&\iff \exists x (\neg \phi \implies \psi) \tag{0.1} &\iff \exists x (\phi \implies \psi) \tag{0.1}
\end{align*} \end{align*}
$$ $$
**2.** Show that $\phi \implies (\exists x \psi)$ is equivalent to $\exists x (\phi \implies \psi)$ **2.** Show that $\phi \implies (\exists x \psi)$ is equivalent to $\exists x (\phi \implies \psi)$