let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs Y,BOOLEAN holds a 'nand' (b 'nor' c) = (('not' a) 'or' b) 'or' c
let a, b, c be Element of Funcs Y,BOOLEAN ; :: thesis: a 'nand' (b 'nor' c) = (('not' a) 'or' b) 'or' c
thus a 'nand' (b 'nor' c) = a 'nand' ('not' (b 'or' c)) by Th2
.= 'not' (a '&' ('not' (b 'or' c))) by Th1
.= ('not' a) 'or' ('not' ('not' (b 'or' c))) by BVFUNC_1:17
.= (('not' a) 'or' b) 'or' c by BVFUNC_1:11 ; :: thesis: verum