Is there an obvious inconsistency with the following first order set theory?
Axioms:
Extensionality as in ZF.
Foundation as in ZF.
Hereditary comprehension: if $\leq$ is a binary relation symbol, and $\phi$ is a formula in which all of its free variables are among symbols $``y,\vec{w},l"$, then: $$\leq \text { is a non-strict partial order} \land (\subseteq \implies \leq) \\ \implies \forall \vec{w} \forall l \exists x \forall y (y \in x \leftrightarrow y \leq^h l \land \phi)$$; Where $\leq^h$ signify "hereditarily $\leq$", defined as: $$y \leq^h l \iff y \leq l \land \forall x \in TC(y): x \leq l$$; and where $TC$ stands for transitive closure operator defined as the minimal transitive superset of a set, that is: $$TC(x)=t \iff x \subseteq t \land transitive(t) \land \forall s (x \subseteq s \land transitive(s) \to t \subseteq s)$$; where transitive set is a set whose elements are subsets of it.
The reason why I'm asking this question is that the above theory prove all axioms of Zermelo set theory. However, I think that one can perhaps even prove all axioms of $\sf ZF$. Howover I suspect that the restriction in the antedecdent of comprehension is too light that there is a high chance that an inconsistency can pentrate through.
The more general context of this question is about what qualification we can impose on $\leq$ in order to prevent inconsistency and yet get a theory that can interpret $\sf ZF$ or even stronger extensions.