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
  the_left_argument_of F <=> G = F => G & the_right_argument_of F <=> G
  = G => F by Th4;
