A book I am reading has a section on probability density function.

Random var Xi is drawn from a pdf p(x)

Random var Yi is drawn from y(Xi), a one to one function with strictly positive or negative derivative.

The book I read claims

Pr( Y <= y(x) ) = Pr( X <= x )

Which I am not understanding how it is derived. Notice It does not make much distinction of X, Xi, and Y, Yi.

Pr is the CDF. The goal of this section is to find the pdf of a transformed random var. The final formula is

p(y) = |dy/dx|^-1 * q(x)

Thanks