If you substitute NATO for the EU in your statement, it might make sense, but NATO has many non-EU members, including the most powerful member by far.
You forget that NATO includes Turkey which invaded Cyprus, which at that time was under the effective control of NATO member Greece.
No EU (or its pre-1993 or 1986 iterations) member state has ever gone to war with another EU member state. Fact.
No worries on the Brexit intrusion, it's important stuff.