Existential Generalisation/Proof System

Theorem
Let $\map {\mathbf A} x$ be a WFF of predicate Logic of $\LL$.

Let $\tau$ be a term which is freely substitutable for $x$ in $\mathbf A$.

Let $\mathscr H$ be Hilbert proof system instance 1 for predicate logic.

Then:


 * $\map {\mathbf A} \tau \vdash_{\mathscr H} \exists x: \map {\mathbf A} x$

is a provable consequence in $\mathscr H$.