let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'nand' (a 'or' b) = ('not' a) '&' ('not' (a '&' b))
let a, b be Function of Y,BOOLEAN; :: thesis: a 'nand' (a 'or' b) = ('not' a) '&' ('not' (a '&' b))
thus a 'nand' (a 'or' b) = ('not' (a '&' a)) '&' ('not' (a '&' b)) by th11
.= ('not' a) '&' ('not' (a '&' b)) ; :: thesis: verum