theorem EasyAngleTransport:
  o <> a implies
    ex x,y st between b,o,x & between a,o,y & x,y,o cong a,b,o
   proof
     assume
X1:  o <> a;
     consider x such that
X2:  between b,o,x & o,x equiv o,a by A4;
     x,o equiv a,o by X2, CongruenceDoubleSymmetry; then
X5:  a,o,x cong x,o,a by X2, A1, EquivSymmetric;
     consider y such that
X6:  between a,o,y & o,y equiv o,b by A4;
     between x,o,b by X2, Bsymmetry; then
     x,y,o cong a,b,o by X6, CongruenceDoubleSymmetry, X1, X5, A5;
     hence thesis by X2, X6;
   end;
