reserve x,y,x1,x2,z for set,
  n,m,k for Nat,
  t1 for (DecoratedTree of [: NAT,NAT :]),
  w,s,t,u for FinSequence of NAT,
  D for non empty set;
reserve s9,w9,v9 for Element of NAT*;

theorem Th21:
  MP-conectives misses MP-variables
proof
  assume not thesis;
  then consider x being object such that
A1: x in [:{0,1,2},NAT:] and
A2: x in [:{3},NAT:] by XBOOLE_0:3;
  consider x1,x2 being object such that
A3: x1 in {0,1,2} and
  x2 in NAT and
A4: x = [x1,x2] by A1,ZFMISC_1:def 2;
  x1 = 3 by A2,A4,ZFMISC_1:105;
  hence contradiction by A3,ENUMSET1:def 1;
end;
