theorem Th52:
  p1,p2 split P & q in P & q <> p2 implies q,p2 split P
proof
  assume that
A1: p1,p2 split P and
A2: q in P and
A3: q <> p2;
  p2,p1 split P by A1,Th50;
  then p2,q split P by A2,A3,Th51;
  hence thesis by Th50;
end;
