There is an intention in IDEA to extract inline CSS from the style attribute, for example
to a CSS selector
However nice in theory, the feature currently is practically useless:
First, it always only extracts to a style section in the same file.
Even worse it does not allow to create a class or id selector. No, thanks, I don't want bold in all my divs.
There are already issues in Jira, but they are soon celebrating their second birthday, so please comment on or vote for
IDEADEV-11966 - Offer to create CSS class in "Extract embedded CSS" dialog: http://www.jetbrains.net/jira/browse/IDEADEV-11966
IDEADEV-11964 - Allow user to select which CSS file or style block should be used in "Extract embedded CSS": http://www.jetbrains.net/jira/browse/IDEADEV-11964