 reserve X,a,b,c,x,y,z,t for set;
 reserve R for Relation;

theorem Th5A:
  for R being non empty RelStr,
      a, b being Element of R st
    [a,b] in the InternalRel of R holds a in UAp {b}
  proof
    let R be non empty RelStr;
    let a, b be Element of R;
B1: b in {b} by TARSKI:def 1;
    assume [a,b] in the InternalRel of R; then
B3: b in Class (the InternalRel of R,a) by RELAT_1:169;
    reconsider B = {b} as Subset of R;
B2: Class (the InternalRel of R,a) meets B by B3,B1,XBOOLE_0:3;
    UAp B = { x where x is Element of R : Class (the
      InternalRel of R, x) meets B } by ROUGHS_1:def 5;
    hence thesis by B2;
  end;
