reserve A, B for non empty preBoolean set,
  x, y for Element of [:A,B:];
reserve X for set,
  a,b,c for Element of [:A,B:];

theorem Th1:
  a c= b & b c= a implies a = b
proof
  assume a`1 c= b`1 & a`2 c= b`2 & b`1 c= a`1 & b`2 c= a`2;
  then a`1 = b`1 & a`2 = b`2;
  hence thesis by DOMAIN_1:2;
end;
