Why in the Deduction Theorem do we require a closed formula?
Deduction Theorem. Let $A$ be a closed formula in $T$. For every formula $B$ of $T$, $\vdash_T A \implies B$ iff $B$ is a theorem of $T[A]$.
I could not find any counterexample.
Can you explain me where is the problem?
I found a counterexample.
if $A=C$ and $B=\forall(x)C$
when A is not a closed formula.