reserve X for BCI-algebra;
reserve I for Ideal of X;
reserve a,x,y,z,u for Element of X;
reserve f,f9,g for sequence of  the carrier of X;
reserve j,i,k,n,m for Nat;
reserve R for Equivalence_Relation of X;
reserve RI for I-congruence of X,I;
reserve E for Congruence of X;
reserve RC for R-congruence of X;
reserve LC for L-congruence of X;

theorem
  IConSet(X) c= ConSet(X)
proof
  let x be object;
  assume x in IConSet(X);
  then ex I being Ideal of X st x is I-congruence of X,I by Def13;
  hence thesis;
end;
