Did you not get as far as the sentence immediately following the one you quoted? I listed a bunch of likely reasons for there being no War between EU countries.

Just because the EU happened to exist during a period of peace, does not mean it is the reason for it. There was a little thing called World War 2 that may also have played a part.

Care to point out the last war between two first world democratic countries?

Given that 'first world' means 'US and its allies', that's clearly a loaded question. There was no war between second-world communist countries either.

If you take out the 'first world' bit, then yes, there's been plenty of war between democracies, including World War I: http://users.erols.com/mwhite28/demowar.htm

"First world" nowadays effectively includes much of the original "Third world" (such as Sweden, Finland, Austria, Switzerland, France, Yugoslavia or Mexico ).

How many of those communist countries were democracies though?

I think my point stands, it's pretty rare for democracies to go to war. If you take the example of WW1, I doubt many people would consider Germany to have been a democracy in our modern understanding of the word.

Anyway where's your evidence that the EU somehow prevents war?

There's nothing to stop the EU going to war with someone else (when they get a military) for starters.