theorem Th49:
  a,b congr c,d implies a,c '||' b,d
proof
  assume
A1: a,b congr c,d;
A2: now
    assume
A3: a=b;
    then c =d by A1,Th45;
    hence thesis by A3,PARSP_1:25;
  end;
  a<>b implies thesis by A1,Th39;
  hence thesis by A2;
end;
