Prince Harry got a leg up ... 'cause he's a good boy. Yes, he is!!

Harry greeted British war hero Phillip Eaglesham and his service dog, Copper, at a Heads Together event -- a mental health initiative set up by Harry, Prince William and Kate. The royal fam hosted the event in honor of Tuesday being World Mental Health Day.

Hard to tell from the pics who's more impressive in this meeting here.

Then again, we're sure Harry would do a few tricks too ... for the right treat.