Procs and double attack

[Varren]

Proc rate is a fixed chance per swing based on delay and dex to produce an average number of procs per period of time, but how does double attack figure in? I don’t think I’ve seen two procs per round with one hand, but I may have missed it. Does proc only happen on the first initiated swing and never on the double/triple attack?

I was puzzling over this while swinging away on my cleric today, who will forever be limited to one attack per round.

Thanks seers.