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 Th38:
  Class(RI,0.X) c= I
proof
  let x be object;
  assume
A1: x in Class(RI,0.X);
  then consider y being object such that
A2: [y,x] in RI and
A3: y in {0.X} by RELAT_1:def 13;
  reconsider x as Element of X by A1;
  reconsider y as Element of X by A3,TARSKI:def 1;
  y=0.X by A3,TARSKI:def 1;
  then x\0.X in I by A2,Def12;
  hence thesis by BCIALG_1:2;
end;
