reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;
reserve F,F1,G,G1,H,H1 for ZF-formula;
reserve sq,sq9 for FinSequence;

theorem Th34:
  Ex(x,H) = Ex(y,G) implies x = y & H = G
proof
  assume Ex(x,H) = Ex(y,G);
  then
A1: All(x,'not' H) = All(y,'not' G) by FINSEQ_1:33;
  then 'not' H = 'not' G by Th3;
  hence thesis by A1,Th3,FINSEQ_1:33;
end;
