Can the Chase test algorithm only modify attributes on the right side of a functional dependency?

Question

I'm attempting to apply the Chase Algorithm to determine if a decomposition is a lossless join decomposition.

Functional Dependencies = {A → C, B → D, C → D, DE → C, CE → A}

Here is my initial matrix:

Can I apply DE → C to remove the subscript from e on the first two rows? Since all c₁'s are the same, then this means that e₁ and e₂ must be equivalent to e, correct?

At this point, I would be able to set all c₁'s equal to c, correct? (Since, again, DE → C.)