let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a 'xor' (a 'nor' b) = a 'or' ('not' b)
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: a 'xor' (a 'nor' b) = a 'or' ('not' b)
thus a 'xor' (a 'nor' b) = (a 'or' ('not' (a 'or' b))) '&' ((('not' a) 'or' a) 'or' b) by Th64
.= (a 'or' ('not' (a 'or' b))) '&' ((I_el Y) 'or' b) by BVFUNC_4:6
.= (a 'or' ('not' (a 'or' b))) '&' (I_el Y) by BVFUNC_1:13
.= a 'or' ('not' (a 'or' b)) by BVFUNC_1:9
.= a 'or' (('not' a) '&' ('not' b)) by BVFUNC_1:16
.= (a 'or' ('not' a)) '&' (a 'or' ('not' b)) by BVFUNC_1:14
.= (I_el Y) '&' (a 'or' ('not' b)) by BVFUNC_4:6
.= a 'or' ('not' b) by BVFUNC_1:9 ; :: thesis: verum