let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds 'not' (a 'or' b) = ('not' a) '&' ('not' b)
let a, b be Function of Y,BOOLEAN; :: thesis: 'not' (a 'or' b) = ('not' a) '&' ('not' b)
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: ('not' (a 'or' b)) . x = (('not' a) '&' ('not' b)) . x
thus ('not' (a 'or' b)) . x = 'not' ((a 'or' b) . x) by MARGREL1:def 19
.= 'not' ((a . x) 'or' (b . x)) by Def4
.= (('not' a) . x) '&' ('not' (b . x)) by MARGREL1:def 19
.= (('not' a) . x) '&' (('not' b) . x) by MARGREL1:def 19
.= (('not' a) '&' ('not' b)) . x by MARGREL1:def 20 ; :: thesis: verum