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 All(x,y,z,H) = variables_in H \/ {x,y,z}
proof
  thus variables_in All(x,y,z,H) = variables_in All(y,z,H) \/ {x} by Th142
    .= variables_in H \/ {y,z} \/ {x} by Th147
    .= variables_in H \/ ({y,z} \/ {x}) by XBOOLE_1:4
    .= variables_in H \/ {y,z,x} by ENUMSET1:3
    .= variables_in H \/ {x,y,z} by ENUMSET1:59;
end;
