let A be non degenerated commutative Ring; :: thesis: nilrad A = meet (Spectrum A)
reconsider I = {(0. A)} as proper Ideal of A by SUBSET_1:def 6;
nilrad A = sqrt {(0. A)} by Th27
.= meet (PrimeIdeals (A,I)) by Th28
.= meet (Spectrum A) by Th21 ;
hence nilrad A = meet (Spectrum A) ; :: thesis: verum