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
  p 'or' q = p1 'or' q1 implies p = p1 & q = q1
proof
  assume p 'or' q = p1 'or' q1;
  then 'not' p '&' 'not' q = 'not' p1 '&' 'not' q1 by FINSEQ_1:33;
  then 'not' p = 'not' p1 & 'not' q = 'not' q1 by Th2;
  hence thesis by FINSEQ_1:33;
end;
