Finally I proved it this way, first we need a few definitions:
$co-W = \{A | \overline{A} \in W\}$
set $W$ is called m-closed if for $A \in W$, and for any $B \leq_mA$ then $B \in W$
We already knew (Davis book page 209)
If $W$ is m-closed or 1-closed then so is $co-W$
Because the set of all $r.e.$ sets is m-closed so is $co-r.e.$,
$A \in r.e. \rightarrow \overline{A}\in co-r.e.$ //by definition
$A \leq_m \overline{A}$ because $\overline{A} \in co-r.e.$ and $co-r.e.$ set is m-closed so $A \in co-r.e.$
$A \in co-r.e.$ it implies $\overline{A} \in r.e.$
$A \in r.e. \land \overline{A}\in r.e. \rightarrow A \in recursive$
and the proof is completed
It implies any set $\psi$ that is m-closed or 1-closed, if $A\in\psi$ and $A \leq_m \overline{A}$ or $A\in\psi$ and $A \leq_1 \overline{A}$, then $\overline{A}\in\psi$