let x be object ; :: thesis: for V, A being set st x in (ND (V,A)) \ A holds
x is NonatomicND of V,A
let V, A be set ; :: thesis: ( x in (ND (V,A)) \ A implies x is NonatomicND of V,A )
assume A1: x in (ND (V,A)) \ A ; :: thesis: x is NonatomicND of V,A
then x in ND (V,A) ;
then A2: ex w being TypeSCNominativeData of V,A st x = w ;
not x in A by A1, XBOOLE_0:def 5;
hence x is NonatomicND of V,A by A2, Def6; :: thesis: verum