MHB Can you prove $C\lor D$ using given premises?

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The discussion presents a logical problem requiring the proof of $C \lor D$ from the premises $A \lor B$, $A \to C$, and $\neg D \to \neg B$. Participants are encouraged to use any valid first-order deduction system, specifying which one they choose. The thread highlights a lack of responses to the problem, indicating a desire for engagement from members, particularly Evgeny. The original poster shares their answer, contributing to the ongoing discourse. The focus remains on logical deduction and the application of formal proof techniques.
Ackbach
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Here's this week's problem.

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From $A\lor B, \; A \to C, \; \neg D \to \neg B$, prove
$C\lor D$. You may use any valid first-order deduction system, but you
must indicate which one you are using (Copi's 19 Rules, Natural
Deduction, etc.).

-----

Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
 
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No one answered this week's Undergraduate POTW; I was hoping this problem could at least tempt Evgeny! ;)

Here is my answer:

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