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 Th2:
  a c= b & b c= c implies a c= c
proof
  assume a`1 c= b`1 & a`2 c= b`2 & b`1 c= c`1 & b`2 c= c`2;
  hence a`1 c= c`1 & a`2 c= c`2;
end;
