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 Th92:
  T is S4_theory iff CnS4(T) = T
proof
  hereby
    assume
A1: T is S4_theory;
A2: CnS4(T) c= T
    by A1,Def23;
    T c= CnS4(T) by Th89;
    hence CnS4(T) = T by A2,XBOOLE_0:def 10;
  end;
  thus thesis;
end;
