Solve the left side and show exact steps to solve. Also, can you use algebraic terms for each step " Distributive property or Associative Multiplicative property" as of that

Ok, so
Given that:
[tex]\begin{gathered} m+n=p \\ p=3r \\ m=n \end{gathered}[/tex]We have to prove that:
[tex]3r=2n[/tex]Notice that if m = n, then,
[tex]\begin{gathered} m+n=p \\ n+n=p \\ 2n=p \end{gathered}[/tex]We also know that p=3r, so:
[tex]\begin{gathered} 2n=p=3r \\ \end{gathered}[/tex]Therefore,
[tex]3r=2n[/tex]