let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a '&' b = (a 'nand' b) 'nand' (a 'nand' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a '&' b = (a 'nand' b) 'nand' (a 'nand' b)
thus (a 'nand' b) 'nand' (a 'nand' b) = 'not' ((a 'nand' b) '&' (a 'nand' b)) by th1
.= (a '&' b) 'or' ('not' ('not' (a '&' b))) by th1
.= a '&' b ; :: thesis: verum