let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN st a 'imp' (b 'imp' c) = I_el Y & a 'imp' b = I_el Y & a = I_el Y holds
c = I_el Y
let a, b, c be Function of Y,BOOLEAN; :: thesis: ( a 'imp' (b 'imp' c) = I_el Y & a 'imp' b = I_el Y & a = I_el Y implies c = I_el Y )
assume that
A1: a 'imp' (b 'imp' c) = I_el Y and
A2: a 'imp' b = I_el Y and
A3: a = I_el Y ; :: thesis: c = I_el Y
for x being Element of Y holds c . x = TRUE

proof

let x be Element of Y; :: thesis: c . x = TRUE
(a 'imp' (b 'imp' c)) . x = TRUE by A1, BVFUNC_1:def 11;
then ('not' (a . x)) 'or' ((b 'imp' c) . x) = TRUE by BVFUNC_1:def 8;
then A4: ('not' (a . x)) 'or' (('not' (b . x)) 'or' (c . x)) = TRUE by BVFUNC_1:def 8;
(a 'imp' b) . x = TRUE by A2, BVFUNC_1:def 11;
then ('not' (a . x)) 'or' (b . x) = TRUE by BVFUNC_1:def 8;
then FALSE 'or' (b . x) = TRUE by A3, BVFUNC_1:def 11, MARGREL1:11;
then b . x = TRUE by BINARITH:3;
then FALSE 'or' (('not' TRUE) 'or' (c . x)) = TRUE by A4, A3, BVFUNC_1:def 11, MARGREL1:11;
then FALSE 'or' (FALSE 'or' (c . x)) = TRUE by MARGREL1:11;
then FALSE 'or' (c . x) = TRUE by BINARITH:3;
hence c . x = TRUE by BINARITH:3; :: thesis: verum

end;

hence c = I_el Y by BVFUNC_1:def 11; :: thesis: verum