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

theorem Th106:
  X c= A \ B implies X c= A & X misses B
proof
  assume
A1: X c= A \ B;
  A \ B c= A by Th36;
  hence X c= A by A1;
  now
    let x be object;
    assume x in X;
    then x in A \ B by A1;
    hence not x in B by XBOOLE_0:def 5;
  end;
  hence thesis by XBOOLE_0:3;
end;
