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 Th97:
  A\iffB\andC in F & C\iffD in F implies A\iffB\andD in F
  proof
    assume A1: A\iffB\andC in F;
    then A2: B\andC\iffA in F by Th90;
    assume C\iffD in F;
    then C\impD in F & D\impC in F & B\impB in F by Th43,Th34;
    then B\andC\impB\andD in F & B\andD\impB\andC in F by Th72;
    then A\impB\andD in F & B\andD\impA in F by A1,A2,Th92,Th93;
    hence A\iffB\andD in F by Th43;
  end;
