Let r be a polynomial ring over an infinite field k and i a

Question

Question: Let R be a polynomial ring over an infinite field k and I a graded ideal of height r. If I is minimally generated by forms of degree p ≥ 1, prove that there are forms f₁,...,f_m of degree p in I such that f₁,...,f_r is a regular sequence and I is minimally generated by f₁,...,f_m.