let Y be non empty set ; :: thesis: for a, b being Element of Funcs Y,BOOLEAN st b = I_el Y holds
a 'imp' b = I_el Y
let a, b be Element of Funcs Y,BOOLEAN ; :: thesis: ( b = I_el Y implies a 'imp' b = I_el Y )
assume A1: b = I_el Y ; :: thesis: a 'imp' b = I_el Y
for x being Element of Y holds (a 'imp' b) . x = TRUE

proof

let x be Element of Y; :: thesis: (a 'imp' b) . x = TRUE
b . x = TRUE by A1, BVFUNC_1:def 14;
then (a 'imp' b) . x = ('not' (a . x)) 'or' TRUE by BVFUNC_1:def 11
.= TRUE by BINARITH:19 ;
hence (a 'imp' b) . x = TRUE ; :: thesis: verum

end;

hence a 'imp' b = I_el Y by BVFUNC_1:def 14; :: thesis: verum