let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a '&' b = (a 'nand' b) 'nand' (a 'nand' b)
let a, b be Element of Funcs (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