let X1, X2, X3, X4, X5, X6 be set ; :: thesis: ( ( X1 <> {} & X2 <> {} & X3 <> {} & X4 <> {} & X5 <> {} & X6 <> {} ) iff [:X1,X2,X3,X4,X5,X6:] <> {} )
( ( X1 <> {} & X2 <> {} & X3 <> {} & X4 <> {} & X5 <> {} ) iff [:X1,X2,X3,X4,X5:] <> {} ) by Th13;
hence ( ( X1 <> {} & X2 <> {} & X3 <> {} & X4 <> {} & X5 <> {} & X6 <> {} ) iff [:X1,X2,X3,X4,X5,X6:] <> {} ) by ZFMISC_1:90; :: thesis: verum