let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'nor' (a 'nor' b) = ('not' a) '&' b
let a, b be Function of Y,BOOLEAN; :: thesis: a 'nor' (a 'nor' b) = ('not' a) '&' b
thus a 'nor' (a 'nor' b) = ('not' a) '&' (a 'or' b) by Th38
.= (('not' a) '&' a) 'or' (('not' a) '&' b) by BVFUNC_1:12
.= (O_el Y) 'or' (('not' a) '&' b) by BVFUNC_4:5
.= ('not' a) '&' b by BVFUNC_1:9 ; :: thesis: verum