We have beta-reduction (λx. M)N = M[N/x] where M[N/x] is M with N substituted for x. Then

⌈if T then u else v⌉ = Tuv (by definition of "if")

= (λxλy. x)uv (by definition of T)

= ((λy. x)[u/x])v

= (λy. u)v

= u

"if F then u else v" is considered similarly.