Need Help with Propositional Logic I am stuck with this proof. I am trying to use deduction (or induction I think) to prove for a tautology with logic laws like De Morgan's, distributive , and implication law etc. 
Note: I am not allowed to use truth tables.
Here it is:
$((p \vee q) \wedge (p \rightarrow r) \wedge (q \rightarrow r)) \rightarrow r$
I have tried using a condition/implication law where $p \rightarrow r$ becomes $\neg p \vee r$ to change the last to compound statements but I got stuck.
Next I tried:
$((p \vee q) \wedge (p \rightarrow r) \wedge (q \rightarrow r)) \rightarrow r \\ \equiv [(p \vee q) \wedge ((p \vee q) \rightarrow r)] \rightarrow r$
But I don't know where to go from here.
Need some guidance guys.

Hint: $((p\vee q)\wedge ((p\vee q)\to r))\to r 
\\\iff\\
 ((p\vee q)\wedge (\neg(p\vee q)\vee r) )\to r
$
