let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a '&' (a 'nand' b) = a '&' ('not' b)
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: a '&' (a 'nand' b) = a '&' ('not' b)
thus a '&' (a 'nand' b) = (a '&' ('not' a)) 'or' (a '&' ('not' b)) by Th50
.= (O_el Y) 'or' (a '&' ('not' b)) by BVFUNC_4:5
.= a '&' ('not' b) by BVFUNC_1:9 ; :: thesis: verum