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 Th72:
  A\impB in F & C\impD in F implies A\andC\impB\andD in F
  proof
    assume A1: A\impB in F;
    assume A2: C\impD in F;
A3: A\andC\impB\imp(A\andC\impD\imp(A\andC\impB\andD)) in F by Th49;
    A\andC\impA in F & A\andC\impC in F by Def38; then
A4: A\andC\impB in F & A\andC\impD in F by A1,A2,Th45; then
    A\andC\impD\imp(A\andC\impB\andD) in F by A3,Def38;
    hence A\andC\impB\andD in F by A4,Def38;
  end;
