reserve T, X, Y for Subset of MC-wff;
reserve p, q, r, s for Element of MC-wff;
reserve T, X, Y for Subset of MC-wff;
reserve p, q, r for Element of MC-wff;
reserve T, X, Y for Subset of MC-wff;
reserve p, q, r for Element of MC-wff;

theorem Th87:
  p in CnS4 (X) implies Nes p in CnS4 (X)
proof
  assume
A1: p in CnS4 (X);
  T is S4_theory & X c= T implies Nes p in T
  proof
    assume that
A2: T is S4_theory and
A3: X c= T;
    p in T by A1,A2,A3,Def23;
    hence thesis by A2;
  end;
  hence thesis by Def23;
end;
