Can someone help me with this discrete mathematics problem?

Use resolution to show the hypotheses "Allen is a bad boy or Hillary is a good girl" and "Allen is a good boy or David is happy" imply the conclusion "Hillary is a good girl or David is happy."

Let P = "Allen is a good boy"
Q = "Hillary is a good girl"
R = "David is happy"

Given:
~PVQ
PVR
Prove:
QVR

RVP
by Commutativity

~~RVP
by Double Negation

If ~R then P
by Material Implication

If P then Q
by Material Implication

If ~R then Q
by Hypothetical Syllogism

~~R V Q
by Material Implication

RVQ
by Double Negation

QVR
by Commutativity

Hence, it was proven. :D