since now this worked fine.
When $mysqlStatement was of type mysqli, i could use $mysqlStatement->execute() or $mysqlStatement->bind_param(.....) and so on, no errors.
Since the newest EAP 6 of phpstorm, all methods are marked as "Method 'execute' not found in class....".
Did I do a mistake, or am I missing something, or is that a new bug that hasn´t been there in the last version?
Thank you a lot.