theorem Th49:
  p is biconditional implies Vars(p,V) = Vars(the_left_side_of p,V
  ) \/ Vars(the_right_side_of p,V)
proof
  set p1 = the_left_side_of p;
  set p2 = the_right_side_of p;
  assume p is biconditional;
  then p = p1 <=> p2 by QC_LANG2:39;
  then p = (p1 => p2) '&' (p2 => p1) by QC_LANG2:def 4;
  hence Vars(p,V) = Vars(p1 => p2, V) \/ Vars(p2 => p1, V) by Th42
    .= Vars(p1,V) \/ Vars(p2,V) \/ Vars(p2 => p1, V) by Th48
    .= Vars(p1,V) \/ Vars(p2,V) \/ (Vars(p1,V) \/ Vars(p2,V)) by Th48
    .= Vars(the_left_side_of p,V) \/ Vars(the_right_side_of p,V);
end;
