let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds a 'imp' ('not' a) = 'not' a
let a be Function of Y,BOOLEAN; :: thesis: a 'imp' ('not' a) = 'not' a
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a 'imp' ('not' a)) . x = ('not' a) . x
(a 'imp' ('not' a)) . x = ('not' (a . x)) 'or' (('not' a) . x) by BVFUNC_1:def 8
.= (('not' a) . x) 'or' (('not' a) . x) by MARGREL1:def 19
.= ('not' a) . x ;
hence (a 'imp' ('not' a)) . x = ('not' a) . x ; :: thesis: verum