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