context-free language : if yx belongs to cfl then xy is also cfl

I faced a problem. What is the proof to say that if yx is in a Context-Free Language we can say that xy is also in a context-free language.

C is a Context-Free Language.

xy where yx belongs to C(Context-free language)

I think we can use the PDA defining C and edit final states.

Any ideas? thank you.