Converting Kuroda normal form rules to the Penttonen normal form
You can find the proof in Penttonen's original research article: 

Martti Penttonen, One-Sided and Two-Sided Context in Formal Grammars. Information and Control 25, pp. 371-392 (1974). https://doi.org/10.1016/S0019-9958(74)91049-3