I really don't think it should be.
$dU = dQ + dW$ is the statement of the first law of Thermodynamics.
$dW$ can be put as $-pdV$ and $dQ $can be put as $TdS$ only if the process is reversible. (From the definition of entropy, the $dQ$ in $dS$ = $\frac{dQ}{T}$ is for reversible paths between the inital and final states.)
But when I checked on the net, it says $dU= TdS- pdV$ is always true for any type of process. How? Many say because it contains state variables?
We assumed the process to be reversible while deriving it, otherwise the most general equation should be $dU ≤ TdS - pdV$, right?
Where ever I see on the net, they used that equation $dU = TdS - PdV$ as something always valid and as a base to derive fancy new equations with partial differentials and stuff.
For example, in page 2 in this pdf: https://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/lecture-notes/5_60_lecture11.pdf