let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'eqv' (b 'nor' c) = ((a 'or' b) 'or' c) '&' (('not' a) 'or' ('not' (b 'or' c)))
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'eqv' (b 'nor' c) = ((a 'or' b) 'or' c) '&' (('not' a) 'or' ('not' (b 'or' c)))
thus a 'eqv' (b 'nor' c) = a 'eqv' ('not' (b 'or' c)) by Th2
.= (a 'or' ('not' ('not' (b 'or' c)))) '&' (('not' a) 'or' ('not' (b 'or' c))) by BVFUNC_6:91
.= ((a 'or' b) 'or' c) '&' (('not' a) 'or' ('not' (b 'or' c))) by BVFUNC_1:8 ; :: thesis: verum