theorem Th93:
  A\impB in F & B\iffC in F implies A\impC in F
  proof
    assume
A1: A\impB in F & B\iffC in F;
    A\iffB\imp(A\impB) in F & A\iffB\imp(B\impA) in F &
    B\iffC\imp(B\impC) in F & B\iffC\imp(C\impB) in F by Def38; then
    B\impC in F by A1,Def38;
    hence thesis by A1,Th45;
  end;
