let A, B, C, D, Z be set ; ( A c= Z & B c= Z & C c= Z & D c= Z implies ((A \/ B) \/ C) \/ D c= Z )
assume that
A1:
A c= Z
and
A2:
B c= Z
and
A3:
C c= Z
; ( not D c= Z or ((A \/ B) \/ C) \/ D c= Z )
(A \/ B) \/ C c= Z
by A1, A2, A3, Lm1;
hence
( not D c= Z or ((A \/ B) \/ C) \/ D c= Z )
by XBOOLE_1:8; verum