let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a 'xor' (a 'nand' b) = ('not' a) 'or' b
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: a 'xor' (a 'nand' b) = ('not' a) 'or' b
thus a 'xor' (a 'nand' b) = (('not' a) '&' ('not' (a '&' b))) 'or' ((a '&' a) '&' b) by Th52
.= (('not' a) 'or' (a '&' b)) '&' (('not' (a '&' b)) 'or' (a '&' b)) by BVFUNC_1:11
.= (('not' a) 'or' (a '&' b)) '&' (I_el Y) by BVFUNC_4:6
.= ('not' a) 'or' (a '&' b) by BVFUNC_1:6
.= (('not' a) 'or' a) '&' (('not' a) 'or' b) by BVFUNC_1:11
.= (I_el Y) '&' (('not' a) 'or' b) by BVFUNC_4:6
.= ('not' a) 'or' b by BVFUNC_1:6 ; :: thesis: verum