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
  H is conditional implies the_antecedent_of H = the_left_argument_of
  the_argument_of H
proof
  assume H is conditional;
  then H = (the_antecedent_of H) => (the_consequent_of H) by ZF_LANG:47;
  then
  the_argument_of H = (the_antecedent_of H) '&' 'not'(the_consequent_of H)
  by Th3;
  hence thesis by Th4;
end;
