let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs (Y,BOOLEAN) holds a 'xor' (b 'nor' c) = (a 'or' ('not' (b 'or' c))) '&' ((('not' a) 'or' b) 'or' c)
let a, b, c be Element of Funcs (Y,BOOLEAN); :: thesis: a 'xor' (b 'nor' c) = (a 'or' ('not' (b 'or' c))) '&' ((('not' a) 'or' b) 'or' c)
thus a 'xor' (b 'nor' c) = a 'xor' ('not' (b 'or' c)) by Th2
.= (a 'or' ('not' (b 'or' c))) '&' (('not' a) 'or' ('not' ('not' (b 'or' c)))) by BVFUNC_8:13
.= (a 'or' ('not' (b 'or' c))) '&' ((('not' a) 'or' b) 'or' c) by BVFUNC_1:8 ; :: thesis: verum