consider x3 being set such that
A1: x3 in X3 by XBOOLE_0:def 1;
consider x12 being set such that
A2: x12 in [:X1,X2:] by XBOOLE_0:def 1;
[x12,x3] in [:[:X1,X2:],X3:] by A2, A1, ZFMISC_1:def 2;
hence not [:X1,X2,X3:] is empty by ZFMISC_1:def 3; :: thesis: verum