The roots of Bessel functions

Question

In Abramowitz Stegun 1972 there is an inequality (9.5.2) for roots of Bessel functions and their derivatives (n is positive): $$ n \leq j^{'}_{n,1} <y^{}_{n,1} < y^{'}_{n,1} < j^{}_{n,1} < j^{'}_{n,2} <... $$ Here first index denotes the order of Bessel function, second - the order of root and " ' " denotes that this is a root of derivative of Bessel function. Can anybody help me and tell how this inequality can be proven, or where can i read about this? Also, I'm very interested even in left part of inequality, when n is integer: $$ n \leq j^{'}_{n,1} $$