let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs Y,BOOLEAN holds a 'nand' (b 'eqv' c) = a 'imp' (b 'xor' c)
let a, b, c be Element of Funcs 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_1:17
.= ('not' a) 'or' ('not' ('not' (b 'xor' c))) by BVFUNC25:12
.= ('not' a) 'or' (b 'xor' c) ;
hence a 'nand' (b 'eqv' c) = a 'imp' (b 'xor' c) by BVFUNC_4:8; :: thesis: verum