let X1, X2, X3, Y1, Y2, Y3 be set ; :: thesis: ( [:X1,X2,X3:] <> {} & [:X1,X2,X3:] = [:Y1,Y2,Y3:] implies ( X1 = Y1 & X2 = Y2 & X3 = Y3 ) )
assume [:X1,X2,X3:] <> {} ; :: thesis: ( not [:X1,X2,X3:] = [:Y1,Y2,Y3:] or ( X1 = Y1 & X2 = Y2 & X3 = Y3 ) )
then ( X1 <> {} & X2 <> {} & X3 <> {} ) by Th35;
hence ( not [:X1,X2,X3:] = [:Y1,Y2,Y3:] or ( X1 = Y1 & X2 = Y2 & X3 = Y3 ) ) by Th36; :: thesis: verum