How to AVERAGEIF not using a range of cells?

I've got a formula that will pull in a number. Sometimes that number will be 0. I want to get the average of the items not counting any zeroes. I want this =AVERAGEIF({formula1, formula2, etc},"<>0"). I haven't been able to figure out a way to feed AVERAGEIF individual values to average. I would think that =AVERAGEIF({3,7,0,4},"<>0") should be possible but again I haven't figured out how to make it work. BTW, the answer to the example should be 4.666 (i.e. 14/3). TIA