let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'nor' (b 'eqv' c) = ('not' a) '&' (b 'xor' c)
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'nor' (b 'eqv' c) = ('not' a) '&' (b 'xor' c)
thus a 'nor' (b 'eqv' c) = 'not' (a 'or' (b 'eqv' c)) by Th2
.= ('not' a) '&' ('not' (b 'eqv' c)) by BVFUNC_1:13
.= ('not' a) '&' ('not' ('not' (b 'xor' c))) by Th12
.= ('not' a) '&' (b 'xor' c) ; :: thesis: verum