Can I use exterior paint over interior paint+primer?

Can I use an interior paint+primer as the primer/undercoat for an exterior paint?

I have an unfinished exterior wood door that I want to paint before installation.

I have some interior paint+primer that was used on my interior trim. I have some exterior paint that was used on the exterior trim. The interior is Valspar, the exterior is Dunn-Edwards Evershield. I’m pretty sure both are 100% acrylic-latex paint. Both are semi-gloss.

My plan is to paint the entire door with the interior paint+primer. Once I’ve applied a few coats and it has thoroughly dried, I’ll then paint the exterior facing side with the exterior paint.

Will I run into any issues painting exterior paint over the interior paint+primer?