reserve X,Y,Z for set, x,y,z for object;
reserve i,j for Nat;
reserve A,B,C for Subset of X;
reserve R,R1,R2 for Relation of X;
reserve AX for Subset of [:X,X:];
reserve SFXX for Subset-Family of [:X,X:];
reserve EqR,EqR1,EqR2,EqR3 for Equivalence_Relation of X;

theorem
  x in Class EqR implies ex y being Element of X st x = Class(EqR,y)
proof
  assume
A1: x in Class EqR;
  then reconsider x as Subset of X;
  consider y such that
A2: y in X and
A3: x = Class(EqR,y) by A1,Def3;
  reconsider y as Element of X by A2;
  take y;
  thus thesis by A3;
end;
