How Do I Prove This Tautology?

[Rome_Leader]

Homework Statement

[ (p or r) & (not(p) or r) ] ---> r is a tautology. Prove this without using truth tables.

Homework Equations

See above. not(p) = !p = p' = the opposite value of p and ---> is an implication.

The Attempt at a Solution

I have made some prior simplification, and that is what I have at present. I don't know where to go from here. Expanding the terms seems to make things too complicated. Is there a shorter way?

Any help would be greatly appreciated!

 

[Rome_Leader]

Nevermind, I've solved it! For anyone interested in the solution, I just had to distribute the implication and then expanding was a lot quicker!