reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);

theorem Th5:
  All(x,p) = All(y,q) implies x = y & p = q
proof
A1: <*[3,0]*>^<*x*>^@p = <*[3,0]*>^(<*x*>^@p) & <*[3,0]*>^<*y*>^@q = <*[3,0]
  *>^( <*y*>^@q) by FINSEQ_1:32;
A2: (<*x*>^@p).1 = x & (<*y*>^@q).1 = y by FINSEQ_1:41;
  assume
A3: All(x,p) = All(y,q);
  hence x = y by A1,A2,FINSEQ_1:33;
  <*x*>^@p = <*y*>^@q by A3,A1,FINSEQ_1:33;
  hence thesis by A2,FINSEQ_1:33;
end;
