let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds (a '&' ('not' a)) 'imp' b = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: (a '&' ('not' a)) 'imp' b = I_el Y
for x being Element of Y holds ((a '&' ('not' a)) 'imp' b) . x = TRUE

proof

let x be Element of Y; :: thesis: ((a '&' ('not' a)) 'imp' b) . x = TRUE
((a '&' ('not' a)) 'imp' b) . x = ('not' ((a '&' ('not' a)) . x)) 'or' (b . x) by BVFUNC_1:def 8
.= ('not' ((a . x) '&' (('not' a) . x))) 'or' (b . x) by MARGREL1:def 20
.= (('not' (a . x)) 'or' ('not' ('not' (a . x)))) 'or' (b . x) by MARGREL1:def 19
.= TRUE 'or' (b . x) by XBOOLEAN:102
.= TRUE ;
hence ((a '&' ('not' a)) 'imp' b) . x = TRUE ; :: thesis: verum

end;

hence (a '&' ('not' a)) 'imp' b = I_el Y by BVFUNC_1:def 11; :: thesis: verum