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

proof

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

end;

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