let X1, X2, X3, X4, X5, X6, X7, X8 be set ; :: thesis: ( ( X1 <> {} & X2 <> {} & X3 <> {} & X4 <> {} & X5 <> {} & X6 <> {} & X7 <> {} & X8 <> {} ) iff [:X1,X2,X3,X4,X5,X6,X7,X8:] <> {} )
( ( X1 <> {} & X2 <> {} & X3 <> {} & X4 <> {} & X5 <> {} & X6 <> {} & X7 <> {} ) iff [:X1,X2,X3,X4,X5,X6,X7:] <> {} ) by MC352;
hence ( ( X1 <> {} & X2 <> {} & X3 <> {} & X4 <> {} & X5 <> {} & X6 <> {} & X7 <> {} & X8 <> {} ) iff [:X1,X2,X3,X4,X5,X6,X7,X8:] <> {} ) by ZFMISC_1:113; :: thesis: verum