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

proof

let x be Element of Y; :: thesis: (a 'imp' (a 'or' b)) . x = TRUE
(a 'imp' (a 'or' b)) . x = ('not' (a . x)) 'or' ((a 'or' b) . x) by BVFUNC_1:def 8
.= ('not' (a . x)) 'or' ((a . x) 'or' (b . x)) by BVFUNC_1:def 4
.= (('not' (a . x)) 'or' (a . x)) 'or' (b . x)
.= TRUE 'or' (b . x) by XBOOLEAN:102
.= TRUE ;
hence (a 'imp' (a 'or' b)) . x = TRUE ; :: thesis: verum

end;

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