theorem
  A\impB in F & C\impD in F & \notB\or\notD in F implies \notA\or\notC in F
  proof
    assume A1: A\impB in F;
    assume A2: C\impD in F;
    assume A3: \notB\or\notD in F;
    A\impB\imp(\notB\imp\notA) in F & C\impD\imp(\notD\imp\notC) in F
    by Th57; then
    \notB\imp\notA in F & \notD\imp\notC in F by A1,A2,Def38; then
    \notB\or\notD\imp\notA\or\notC in F by Th59;
    hence \notA\or\notC in F by A3,Def38;
  end;
