 reserve X, Y for set, A for Ordinal;

theorem
  succRel(X) \/ succRel(Y) c= succRel(X \/ Y)
proof
  X c= X \/ Y & Y c= X \/ Y by XBOOLE_1:7;
  then succRel(X) c= succRel(X \/ Y) &
    succRel(Y) c= succRel(X \/ Y) by Th1;
  hence thesis by XBOOLE_1:8;
end;
