let A, B, C, D, Z be set ; ( A misses Z & B misses Z & C misses Z & D misses Z implies ((A \/ B) \/ C) \/ D misses Z )
assume that
A1:
A misses Z
and
A2:
B misses Z
and
A3:
C misses Z
; ( not D misses Z or ((A \/ B) \/ C) \/ D misses Z )
(A \/ B) \/ C misses Z
by A1, A2, A3, XBOOLE_1:114;
hence
( not D misses Z or ((A \/ B) \/ C) \/ D misses Z )
by XBOOLE_1:70; verum