let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a '&' (b 'nor' c) = (a '&' ('not' b)) '&' ('not' c)
let a, b, c be Function of Y,BOOLEAN; :: thesis: a '&' (b 'nor' c) = (a '&' ('not' b)) '&' ('not' c)
thus a '&' (b 'nor' c) = a '&' ('not' (b 'or' c)) by Th2
.= a '&' (('not' b) '&' ('not' c)) by BVFUNC_1:13
.= (a '&' ('not' b)) '&' ('not' c) by BVFUNC_1:4 ; :: thesis: verum