let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'nand' (a 'imp' b) = 'not' (a '&' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'nand' (a 'imp' b) = 'not' (a '&' b)
thus a 'nand' (a 'imp' b) = (('not' a) 'or' a) '&' ('not' (a '&' b)) by Th24
.= (I_el Y) '&' ('not' (a '&' b)) by BVFUNC_4:6
.= 'not' (a '&' b) by BVFUNC_1:6 ; :: thesis: verum