$\text{Ordinal Replacement:}$ if $\phi(x,y)$ is a formula in two free variables $x,y$, then:

$\forall x \ [ordinal(x) \to \exists! y \ (ordinal (y) \wedge \phi(x,y)) ] \to \forall A \ (\forall x \in A (ordinal(x)) \to \exists B \ \forall y \ (y \in B \leftrightarrow \exists x \in A \ \phi(x,y))) $

is an axiom.

In English for every set $A$ of von Neumann ordinals and a function $F$ from von Neumann ordinals to von Neumann ordinals, then we can get a set $B$ whose elements are all the $F$-images of elements of $A$.

i.e. we can replace elements of a set of ordinal by ordinals.

Now is full Replacement provable in $\text{Z + Ordinal Replacement}$?