let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds a 'imp' (a '&' a) = I_el Y
let a be Function of Y,BOOLEAN; :: thesis: a 'imp' (a '&' a) = I_el Y
for x being Element of Y holds (a 'imp' (a '&' a)) . x = TRUE

proof

let x be Element of Y; :: thesis: (a 'imp' (a '&' a)) . x = TRUE
(a 'imp' (a '&' a)) . x = TRUE '&' (('not' (a . x)) 'or' (a . x)) by BVFUNC_1:def 8
.= TRUE by XBOOLEAN:102 ;
hence (a 'imp' (a '&' a)) . x = TRUE ; :: thesis: verum

end;

hence a 'imp' (a '&' a) = I_el Y by BVFUNC_1:def 11; :: thesis: verum