theorem
  H1 is Subgroup of H2 & H1 is Subgroup of H3 implies
    H1 is Subgroup of H2 /\ H3
proof
  assume
A1: H1 is Subgroup of H2 & H1 is Subgroup of H3;
  now
    let g;
    assume g in H1;
    then g in H2 & g in H3 by A1,Th40;
    hence g in H2 /\ H3 by Th82;
  end;
  hence thesis by Th58;
end;
