let a, a1, v, v1, v2 be object ; :: thesis: for V, A being set st {v,v1,v2} c= V & {a,a1} c= A holds
ND_ex_4 (v,v1,v2,a,a1) is TypeSCNominativeData of V,A
let V, A be set ; :: thesis: ( {v,v1,v2} c= V & {a,a1} c= A implies ND_ex_4 (v,v1,v2,a,a1) is TypeSCNominativeData of V,A )
assume ( {v,v1,v2} c= V & {a,a1} c= A ) ; :: thesis: ND_ex_4 (v,v1,v2,a,a1) is TypeSCNominativeData of V,A
then ND_ex_4 (v,v1,v2,a,a1) is NonatomicND of V,A by Th55;
hence ND_ex_4 (v,v1,v2,a,a1) is TypeSCNominativeData of V,A by Def6; :: thesis: verum