  We discuss the two-step transitions in superconductors, where the
intermediate state between the Cooper pair state and the normal metal is the
4-fermion condensate, which is called the intertwined vestigial order. We
discuss different types of the vestigial order, which are possible in the
spin-triplet superfluid $^3$He, and the topological objects in the vestigial
phases. Since in $^3$He the order parameter $A_{\alpha i}$ represents the
analog of gravitational tetrads, we suggest that the vestigial states are
possible in quantum gravity. As in superconductors, the fermionic vacuum can
experience two consequent phase transitions. At first transition the metric
appears as the bilinear combination of tetrads $g_{\mu\nu} =\eta_{ab}< \hat
E^a_\mu \hat E^b_\nu>$, while the tetrad order parameter is still absent,
$e_\mu^a=< \hat E^a_\mu> =0$. This corresponds to the bosonic Einstein general
relativity, which emerges in the fermionic vacuum. The nonzero tetrads
$e_\mu^a=< \hat E^a_\mu> \neq 0$ appear at the second transition, where a kind
of the Einstein-Cartan-Sciama-Kibble tetrad gravity is formed. This suggests
that on the levels of particles, gravity acts with different strength on
fermions and bosons.
