Is this set theory equivalent to ZFC?

Consider a variant of set theory with these axioms:

  • Extensionality,
  • Regularity (foundation),
  • Separation,
  • Powerset,
  • Axiom of Choice, and
  • Transitive closure of a set-like relation is set-like.

Note that it does not explicitly postulate Pairing, Union, Infinity and Replacement.

Question: Is this set theory equivalent to $mathrm{ZFC}$?