theorem Th10:
  p |- q iff [Class(PropRel Q,p),Class(PropRel Q,q)] in OrdRel Q
proof
  [p,p] in PropRel Q by Def12;
  then
A1: p in Class(PropRel Q,p) by EQREL_1:19;
  [q,q] in PropRel Q by Def12;
  then
A2: q in Class(PropRel Q,q) by EQREL_1:19;
A3: Class(PropRel Q,p) in Class PropRel Q & Class(PropRel Q,q) in Class
  PropRel Q by EQREL_1:def 3;
  thus p |- q implies [Class(PropRel Q,p),Class(PropRel Q,q)] in OrdRel Q
  proof
    assume p |- q;
    then for p1,q1 holds p1 in Class(PropRel Q,p) & q1 in Class(PropRel Q,q)
    implies p1 |- q1 by A1,A2,A3,Th9;
    hence thesis by A3,Def13;
  end;
  thus thesis by A1,A2,Def13;
end;
