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How can I have a indented new line in math mode? The line after \newindentedline should be indented and start in a new line.

    X \subset Y \Rightarrow \forall x \in X: x \in Y \newindentedline
        \Rightwarrow X \subset Y
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You should read the mathmode document.

To allow linebreaks inside mathmode you need an environment like align (provided by amsmath):

    X \subset Y &\Rightarrow \forall x \in X: x \in Y \\
        &\Rightarrow X \subset Y

For manual (or more accurate) positioning of the alignment (rather than having it line up with some content in the row above), using the following instead:

    &X \subset Y \Rightarrow \forall x \in X: x \in Y \\
    & \hspace{4em} \Rightarrow X \subset Y

where you specify the indent as the argument to \hspace{...}.

To get a unnumbered equation you can use the align* (see the comment of egreg)

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@Werner: Feel free to edit the post ;-) – Marco Daniel Oct 9 '11 at 18:36
I'd suggest split or align*, to be consistent with Sebastian's question. – egreg Oct 9 '11 at 19:06

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