How can I prove $\Gamma\vdash(\psi_1\lor\psi_2)$ is equivalent to $\Gamma\vdash\psi_1$ or $\Gamma\vdash\psi_2$

Question

Hi I'm learning first order logic, and would like to prove that $\Gamma\vdash(\psi_1\lor\psi_2)$ is equivalent to $\Gamma\vdash\psi_1$ or $\Gamma\vdash\psi_2$ using logic axiom of the following:

1. $((\phi_1\to(\phi_2\to\phi_3))\to((\phi_1\to\phi_2)\to(\phi_1\to\phi_3)))$
2. $(\phi_1\to\phi_1)$
3. $(\phi_1\to(\phi_2\to\phi_1))$
4. $(\phi_1\to((\lnot\phi_1)\to\phi_2))$
5. $(((\lnot\phi_1)\to\phi_1)\to\phi_1)$
6. $((\lnot\phi_1)\to(\phi_1\to\phi_2))$
7. $(\phi_1\to((\lnot\phi_2)\to(\lnot(\phi_1\to\phi_2))))$

The equivalent expression for $(\psi_1\lor\psi_2)$ is $((\lnot\psi_1)\to\psi_2)$

Thanks a lot!!!