reserve I for non empty set,
  J for ManySortedSet of I,
  S for non void non empty ManySortedSign,
  i for Element of I,
  c for set,
  A for MSAlgebra-Family of I,S,
  EqR for Equivalence_Relation of I,
  U0,U1,U2 for MSAlgebra over S,
  s for SortSymbol of S,
  o for OperSymbol of S,
  f for Function;

theorem Th3:
  for i be set, I be non empty set, EqR be Equivalence_Relation of
  I, c1,c2 be Element of Class EqR st i in c1 & i in c2 holds c1 = c2
proof
  let i be set, I be non empty set, EqR be Equivalence_Relation of I, c1,c2 be
  Element of Class EqR such that
A1: i in c1 and
A2: i in c2;
  consider x1 be object such that
  x1 in I and
A3: c1 = Class(EqR,x1) by EQREL_1:def 3;
A4: [i,x1] in EqR by A1,A3,EQREL_1:19;
  consider x2 be object such that
  x2 in I and
A5: c2 = Class(EqR,x2) by EQREL_1:def 3;
  [i,x2] in EqR by A2,A5,EQREL_1:19;
  then Class(EqR,x2) = Class(EqR,i) by A1,EQREL_1:35
    .= c1 by A1,A3,A4,EQREL_1:35;
  hence thesis by A5;
end;
