For public-key encryption, why does COA resistance imply CPA resistance? My professor told me:


  If a public-key crypto-system is secure against ciphertext-only attacks,
  then it is also secure against a chosen-plaintext attack.


Why is this true? Is there a proof that confirms this?
I was/am assuming that for public key encryption, COA means "other than the public key, ciphertext only".  Otherwise, any secure symmetric cipher with the key published becomes a "COA resistant" PKE scheme.  With that in mind, access to an encryption oracle cannot possibly help an attacker, since the attacker can already encrypt any plaintext using the public key. $\:$ Therefore, COA resistance implies CPA resistance. $\:$ (for public-key encryption, with my assumption on the definition of COA)