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In Bruno Poizat's Model Theory I found the following proof of ACF's decidability:

1) ACF is $\Sigma_1$, i.e. the set of sentences which are proved by ACF is definable by a $\Sigma_1$ formula.

2) The complement of ACF is also $\Sigma_1$.

3) As a consequence, ACF is $\Delta_1$, hence decidable.

Points (2-3) are clear. Could someone help me proving point (1)? Proving that the set of sentences that axiomatize ACF is $\Sigma_1$ is sufficient.

Thank you in advance.