Six year old had loose tooth, Daddy yanked it with string...?

It had been loose for approx. 3 weeks, driving her nuts. We yanked it out. Couple days later a little white tooth nub shows up behind where the baby tooth was. Do adult teeth come in that fast after a baby tooth is gone? Could it be a piece of her baby tooth that didn't get pulled loose? It doesn't appear to be wiggly. Just curious as our dental insurance doesn't kick in for another month...
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More than likely it is the new tooth coming in that fast, in fact my son has had new teeth PUSH the old one's out. I took him to the dentist after one particularly gruesome baby tooth falling out epsiode and the dentist said that there was some root left in the gums, but not to worry, it would fall out in it's own time and the only times to really be concerned were if there was pain....
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