That's cannibalism

I don't think the original was made with a steel form. In fact, I think the lower arch is working as the form for the upper arch.

Remember that the force on an arch is going outwardly, not downwardly (like with the newer horizontal brick).

The top arch is doing most of the heavy lifting as far as supporting weight. It only needs help keeping the joints on its underside from pulling apart (outwardly force). This is where a steel form comes in, or in this case, the second arch.

The second arch is doing the job of a steel form by keeping the underside of the top arch from spreading. It also likely isn't supporting much weight. You should be fine with no support under the second arch as long as the mortar joints are strong on the underside and at the edges.

EDIT: I should note, I am not a mason, but my dad was. It couldn't hurt to get the opinion of a professional mason before you start pulling bricks.

Check this out. It might answer your question. It also matters how the bricks are laid above the arch, which we can't see from your picture.