reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X9 \/ Y9 = X \/ Y & X misses X9 & Y misses Y9 implies X = Y9
proof
  assume
A1: X9 \/ Y9 = X \/ Y;
  assume X misses X9 & Y misses Y9;
  then
A2: X /\ X9 = {} & Y /\ Y9 = {};
  thus X = X /\ (X9 \/ Y9) by A1,Th7,Th28
    .= X /\ X9 \/ X /\ Y9 by Th23
    .= (X \/ Y) /\ Y9 by A2,Th23
    .= Y9 by A1,Th7,Th28;
end;
