Prove that $\{ \phi \rightarrow(\psi \rightarrow \theta)\} \vdash \phi \wedge \psi \rightarrow \theta$?

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Please, can you check is my solution of this problem $\{ \phi \rightarrow(\psi \rightarrow \theta)\} \vdash \phi \wedge \psi \rightarrow \theta$ good?

First, I rewrote it like $\{ \phi \rightarrow(\psi \rightarrow \theta), \phi \wedge \psi \} \vdash \theta$. After that

1) $\phi \rightarrow(\psi \rightarrow \theta)$ - premise

2) $\phi \wedge \psi $ - assumption

3) $\phi \wedge \psi \rightarrow \phi$ - axiom

4) $\phi$ - Modus Ponens(2,3)

5) $\psi \rightarrow \theta$ - Modus Ponens(4,1)

6) $\phi \wedge \psi \rightarrow\psi$ - axiom

7) $\psi$ - Modus Ponens(6,2)

8) $\theta$ - Modus Ponens (5,7)

And after that I applied $\textit{Deduction theorem}$.