Prove that if $R[x]$ is a PID, then $R$ is a field

Question

I just need someone to check my proof and provide me feedback:

Since $R[x]$ is a PID, then the ideal $I = (x-1)$ generated by the polynomial $x-1$ is maximal because it is of degree 1 added to a constant.

So $R[x]/I\simeq R$ is a field, so $R$ is a field.

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Is this proof enough/correct?

Thanks.