So how close is too close to breed dogs?

So I have four English Bulldogs. I recently took in a new one out of an abusive situation. My intention was to breed her to my male. I just got her pedigree and unfortunately her and my male have the same great grandfather. How ironic!! So, I think it's far enough back that it would be ok. I seriously doubt their would be any deformities. I checked with AKC and they have no rules regarding inbreeding. It's far enough back that it won't even show up on the puppies 3 generation pedigree's. Anyway, what do y'all think about breeding them? I guess they are 3rd cousins.