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;
reserve M for non empty set,
  m,m9 for Element of M,
  v,v9 for Function of VAR,M;
reserve i,j for Element of NAT;

theorem
  variables_in H1 <=> H2 = variables_in H1 \/ variables_in H2
proof
  thus variables_in H1 <=> H2 = variables_in H1 => H2 \/ variables_in H2 => H1
  by Th141
    .= variables_in H1 \/ variables_in H2 \/ variables_in H2 => H1 by Th144
    .= variables_in H1 \/ variables_in H2 \/ (variables_in H1 \/
  variables_in H2) by Th144
    .= variables_in H1 \/ variables_in H2;
end;
