ABC implies a Zsigmondy principle for ramification

Let K be a number field or a function field of characteristic 0. If K is a number field, assume the abc-conjecture for K. We prove a variant of Zsigmondy's theorem for ramified primes in preimage fields of rational functions in K(x) that are not postcritically finite. For example, suppose K is a number field and f∈K[x] is not postcritically finite, and let Kn be the field generated by the nth iterated preimages under f of β∈K. We show that for all large n, there is a prime of K that ramifies in Kn and does not ramify in Km for any m