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 Th158:
  G1 '&' G2 = (H1 '&' H2)/(x,y) iff G1 = H1/(x,y) & G2 = H2/(x,y)
proof
  thus G1 '&' G2 = (H1 '&' H2)/(x,y) implies G1 = H1/(x,y) & G2 = H2/(x,y)
  proof
    assume G1 '&' G2 = (H1 '&' H2)/(x,y);
    then G1 '&' G2 = (H1/(x,y)) '&' (H2/(x,y)) by Lm1;
    hence thesis by ZF_LANG:30;
  end;
  thus thesis by Lm1;
end;
