theorem Th1:
 ex s being set st for p,x holds not [s,[x,p]] in QC-symbols(Al)
proof
  assume
A1: for s being set holds ex p,x st [s,[x,p]] in QC-symbols(Al);
  for s being set holds s in union union QC-symbols(Al)
  proof
    let s be set;
    consider p,x such that
A2:  [s,[x,p]] in QC-symbols(Al) by A1;
A3: {s} in {{s,[x,p]},{s}} by TARSKI:def 2;
A4: s in {s} by TARSKI:def 1;
    {{s,[x,p]},{s}} c= union QC-symbols(Al) by A2,ZFMISC_1:74;
    then {s} c= union union QC-symbols(Al) by A3,ZFMISC_1:74;
    hence thesis by A4;
  end;
  then union union QC-symbols(Al) in union union QC-symbols(Al) &
  for X being set holds not X in X;
  hence contradiction;
end;
