There is a calculation with the conditional expectation in a book I have. I do not understand it, can you please help me? I have taken out the relevant part below:
Let $U_t$ be a stochastic random variable. Let $X$ be a positive stochastic random variable. Let $T_x$ be a stochastic random variable whose distribution is the conditional distribution of $X-x$ given that $X>x$. Last let $t$ be a positive real number. We then have
$E[U_t]\\=E[E[U_t|I_{\{T_x>t\}}]]\\=P(X>x+t|X>x)\cdot E[U_t|T_x>t].$
It is the last equality I do not get, could you please explain it?