reserve n for Element of NAT,
  p,q,r,s for Element of HP-WFF;
reserve V for SetValuation;
reserve P for Permutation of V;

theorem Th35:
  for p9 being Permutation of SetVal(V,p), q9 being Permutation of
SetVal(V,q) st p9 = Perm(P,p) & q9 = Perm(P,q) holds Perm(P,p => q) = p9 => q9
proof
A1: ex p9 being Permutation of SetVal(V,p), q9 being Permutation of SetVal(V
  ,q) st p9 = (Perm P).p & q9 = (Perm P).q & (Perm P).(p '&' q) = [:p9,q9:] & (
  Perm P).(p => q) = p9 => q9 by Def5;
  let p9 be Permutation of SetVal(V,p), q9 be Permutation of SetVal(V,q);
  assume p9 = Perm(P,p) & q9 = Perm(P,q);
  hence thesis by A1;
end;
