We prove that if
f
:
(
R
,
m
)
→
(
S
,
n
)
f: (R,\mathfrak {m}) \rightarrow (S,\mathfrak {n})
is a flat local homomorphism,
S
/
m
S
S/\mathfrak {m} S
is Cohen-Macaulay and
F
F
-injective, and
R
R
and
S
S
share a weak test element, then a tight closure analogue of the (standard) formula for depth and regular sequences across flat base change holds. As a corollary, it follows that phantom depth commutes with completion for excellent local rings. We give examples to show that the analogue does not hold for surjective base change.