let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'nand' (a 'eqv' b) = a 'imp' (a 'xor' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'nand' (a 'eqv' b) = a 'imp' (a 'xor' b)
a 'nand' (a 'eqv' b) = 'not' (a '&' (a 'eqv' b)) by th1
.= ('not' a) 'or' ('not' (a 'eqv' b)) by BVFUNC_1:14
.= ('not' a) 'or' ('not' ('not' (a 'xor' b))) by Th12
.= ('not' a) 'or' (a 'xor' b) ;
hence a 'nand' (a 'eqv' b) = a 'imp' (a 'xor' b) by BVFUNC_4:8; :: thesis: verum