Does multiple condition stop at the first 'false'?

Say a condition has multiple checks like this:

            if (reader != null && !reader.IsClosed)

Does the condition stop if 'reader' is null, or does it continue to even check reader.IsClosed? If it does it would throw an exception because because it's null. Or is this code safe because the 'if' condition breaks as soon as it finds that read is null?
bemara57Asked:
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tigin44Commented:

this is a safe code.
if will function properly even the reader is null as returning false..
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Guy Hengel [angelIII / a3]Billing EngineerCommented:
see this tutorial:
http://www.csharp-station.com/Tutorials/Lesson03.aspx

One difference in the last statement from the others is the boolean expressions. The boolean expression, (myInt < 0 || myInt == 0), contains the conditional OR (||) operator. In both the regular OR (|) operator and the conditional OR (||) operator, the boolean expression will evaluate to true if either of the two sub-expressions on either side of the operator evaluate to true. The primary difference between the two OR forms are that the regular OR operator will evaluate both sub-expressions every time. However, the conditional OR will evaluate the second sub-expression only if the first sub-expression evaluates to false. 
...
The conditional operators (&& and ||) are commonly called short-circuit operators because they do not always evaluate the entire expression. Thus, they are also used to produce more efficient code by ignoring unnecessary logic. 

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