reserve X,Y for set, x,y,z for object, i,j,n for natural number;
reserve
  n for non empty Nat,
  S for non empty non void n PC-correct PCLangSignature,
  L for language MSAlgebra over S,
  F for PC-theory of L,
  A,B,C,D for Formula of L;

theorem Th39: :: Hypothetical syllogism
  (A\impB)\imp((B\impC)\imp(A\impC)) in F
proof
  (B\impC)\imp((A\impB)\imp(A\impC)) in F by Th37;
  hence thesis by Th38;
end;
