An AIRPROX has no separation trigger criteria built in to it. You could actually have an AIRPROX with greater than standard separation between the aircraft at all times. And on the other hand you could have aircraft who do not have standard separation between them, but would not be deemed to be in an AIRPROX situation.
The official definition:
''an Airprox is a situation in which, in the opinion of a pilot or a controller, the distance between aircraft as well as their relative positions and speed have been such that the safety of the aircraft involved was or may have been compromised.''