Intuitionistic logic has the pleasing property that whenever G |- P \/ Q is provable, then either G |- P is provable or G |- Q is provable.

I think this gets to the heart of what is confusing about this example: (London -> England) /\ (Paris -> France) |- (London -> France) \/ (Paris -> England) is classically valid, even though neither (London -> England) /\ (Paris -> France) |- (London -> France) nor (London -> England) /\ (Paris -> France) |- (Paris -> England) is