How to find a logical statement equivalent to the one I have?

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I have the following logical statement
(A \wedge B) \Longleftrightarrow (A \wedge C)
I want to find other logical statements that are equivalent to this. But I don't want to draw truth tables.

Is there a list of 'theorems' that I can look up somewhere? For example, if I have an equivalent statement for D \Longleftrightarrow (A \wedge C), then I can maybe substitute D = (A \wedge B) and maybe come up with something.

Sorry if my terminology is wrong. Logic is not exactly my subject.
 
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That helps. Thanks.
 
I am pretty sure that this is equivalent:
( A \wedge ( B \leftrightarrow C ) )
 

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