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

proof

let x be Element of Y; :: thesis: (('not' (a 'or' b)) 'imp' ('not' a)) . x = TRUE
(('not' (a 'or' b)) 'imp' ('not' a)) . x = ('not' (('not' (a 'or' b)) . x)) 'or' (('not' a) . x) by BVFUNC_1:def 8
.= ('not' ('not' ((a 'or' b) . x))) 'or' (('not' a) . x) by MARGREL1:def 19
.= ((a 'or' b) . x) 'or' ('not' (a . x)) by MARGREL1:def 19
.= ((a . x) 'or' (b . x)) 'or' ('not' (a . x)) by BVFUNC_1:def 4
.= ((a . x) 'or' ('not' (a . x))) 'or' (b . x)
.= TRUE 'or' (b . x) by XBOOLEAN:102
.= TRUE ;
hence (('not' (a 'or' b)) 'imp' ('not' a)) . x = TRUE ; :: thesis: verum

end;

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