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;

theorem
  (H is disjunctive iff ex F,G st H = F 'or' G) & (H is conditional iff
ex F,G st H = F => G) & (H is biconditional iff ex F,G st H = F <=> G) & (H is
  existential iff ex x,H1 st H = Ex(x,H1) );
