reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;

theorem Th9:
  bound_in Ex(x,p) = x & the_scope_of Ex(x,p) = p
proof
  Ex(x,p) is existential;
  then Ex(x,p) = Ex(bound_in Ex(x,p), the_scope_of Ex(x,p)) by ZF_LANG:45;
  hence thesis by ZF_LANG:34;
end;
