let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN st a 'imp' ('not' b) = I_el Y holds
b 'imp' ('not' a) = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: ( a 'imp' ('not' b) = I_el Y implies b 'imp' ('not' a) = I_el Y )
assume A1: a 'imp' ('not' b) = I_el Y ; :: thesis: b 'imp' ('not' a) = I_el Y
for x being Element of Y holds (b 'imp' ('not' a)) . x = TRUE

proof

let x be Element of Y; :: thesis: (b 'imp' ('not' a)) . x = TRUE
(a 'imp' ('not' b)) . x = TRUE by A1, BVFUNC_1:def 11;
then ('not' (a . x)) 'or' (('not' b) . x) = TRUE by BVFUNC_1:def 8;
then A2: ('not' (a . x)) 'or' ('not' (b . x)) = TRUE by MARGREL1:def 19;
(b 'imp' ('not' a)) . x = ('not' (b . x)) 'or' (('not' a) . x) by BVFUNC_1:def 8
.= TRUE by A2, MARGREL1:def 19 ;
hence (b 'imp' ('not' a)) . x = TRUE ; :: thesis: verum

end;

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