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 Th43:
  A\iffB in F iff A\impB in F & B\impA in F
  proof
    (A\iffB)\imp(A\impB) in F & (A\iffB)\imp(B\impA) in F by Def38;
    hence A\iffB in F implies A\impB in F & B\impA in F by Def38;
    assume A\impB in F & B\impA in F;
    then (A\impB)\and(B\impA) in F & (A\impB)\and(B\impA)\imp(A\iffB) in F
    by Def38,Th35;
    hence thesis by Def38;
  end;
