let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds ('not' a) '&' (a 'xor' b) = ('not' a) '&' b
let a, b be Function of Y,BOOLEAN; :: thesis: ('not' a) '&' (a 'xor' b) = ('not' a) '&' b
thus ('not' a) '&' (a 'xor' b) = ('not' a) '&' ((('not' a) '&' b) 'or' (a '&' ('not' b))) by BVFUNC_4:9
.= (('not' a) '&' (('not' a) '&' b)) 'or' (('not' a) '&' (a '&' ('not' b))) by BVFUNC_1:12
.= ((('not' a) '&' ('not' a)) '&' b) 'or' (('not' a) '&' (a '&' ('not' b))) by BVFUNC_1:4
.= (('not' a) '&' b) 'or' ((('not' a) '&' a) '&' ('not' b)) by BVFUNC_1:4
.= (('not' a) '&' b) 'or' ((O_el Y) '&' ('not' b)) by BVFUNC_4:5
.= (('not' a) '&' b) 'or' (O_el Y) by BVFUNC_1:5
.= ('not' a) '&' b by BVFUNC_1:9 ; :: thesis: verum