Basic Derivation using "7 rules"

Question

I'm just checking my work to make sure I'm going through this in a sane fashion:

$P\wedge Q, (P\wedge Q) \rightarrow (R\wedge S), (S\vee U) \rightarrow W \vdash W$

\begin{array}{|c|c|c|c|}\hline\ Scope &Step & Derivation&Rule\\ \hline1&(1)&P\wedge Q& A\\ \hline2&(2)&(P\wedge Q) \rightarrow (R\wedge S)&A \\ \hline3&(3)&(S\vee U) \rightarrow W&A\\ \hline 1,2&(4)&R\wedge S &1,2 \rightarrow E\\ \hline 1,2&(5)&S&4 \wedge E\\ \hline 1,2&(6)&S\vee U&5\vee I\\ \hline 1,2,3&(7)&W&3,6 \rightarrow E \\ \hline \end{array}