reserve A for QC-alphabet;
reserve i,j,k for Nat;
reserve f for Substitution of A;

theorem Th2:
  for x being bound_QC-variable of A, a being free_QC-variable of A holds
   a .--> x is Substitution of A
proof
  let x be bound_QC-variable of A;
  let a be free_QC-variable of A;
  set f = a .--> x;
  rng f = {x} by FUNCOP_1:8;
  then
A1: rng f c= QC-variables(A) by ZFMISC_1:31;
  dom f c= free_QC-variables(A) by ZFMISC_1:31;
  hence thesis by A1,RELSET_1:4;
end;
