let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds 'not' (a '&' ('not' a)) = I_el Y
let a be Function of Y,BOOLEAN; :: thesis: 'not' (a '&' ('not' a)) = I_el Y
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: ('not' (a '&' ('not' a))) . x = (I_el Y) . x
thus ('not' (a '&' ('not' a))) . x = 'not' ((a '&' ('not' a)) . x) by MARGREL1:def 19
.= 'not' ((a . x) '&' (('not' a) . x)) by MARGREL1:def 20
.= 'not' ((a . x) '&' ('not' (a . x))) by MARGREL1:def 19
.= TRUE by XBOOLEAN:102
.= (I_el Y) . x by BVFUNC_1:def 11 ; :: thesis: verum