How can you prove that you are a reviewer for a certain journal. For example, I have been invited to review a paper in a certain journal and on my CV I want to write that I have reviewed in this journal but since reviewers are supposed to be anonymous, how can I supply proof that I have reviewed in this journal?
Reviewers normally receive a confirmation email from the journal editor after submitting a review online. Such email should be sufficient to prove that you have reviewed for the journal.
You don't need to prove it. If someone thinks you're lying, they can just contact the journal editor and check. Reviewers aren't supposed be completely anonymous, anyway. It's just that no one outside of the editors should know who reviewed which articles.
Some journals publish a "thank you to reviewers" list at the end of the year. If your name is on such a list than that establishes that you reviewed for the journal.
As a practical matter, no one is likely to check your CV at this level of detail anyway.
If you don't have any of the other documents by now, just write the publisher and ask him for a letter confirming your being a reviewer.