# Universal Instantiation/Proof System

## Theorem

Let $\map {\mathbf A} x$ be a WFF of predicate logic.

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:

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

is a provable consequence in $\mathscr H$.