let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds a '&' (I_el Y) = a
let a be Function of Y,BOOLEAN; :: thesis: a '&' (I_el Y) = a
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a '&' (I_el Y)) . x = a . x
thus (a '&' (I_el Y)) . x = (a . x) '&' ((I_el Y) . x) by MARGREL1:def 20
.= (a . x) '&' TRUE by Def11
.= a . x ; :: thesis: verum