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 being_equality iff ex x,y st H = x '=' y) & (H is
being_membership iff ex x,y st H = x 'in' y) & (H is negative iff ex H1 st H =
'not' H1) & (H is conjunctive iff ex F,G st H = F '&' G) & (H is universal iff
  ex x,H1 st H = All(x,H1) );
