Resignation after offer letter or contract

Company X is offering me a job. I currently have one, but I would like to switch. So, company X asks me "When would you resign from your current company?" I say "As soon as I receive a formal contract signed by you". One day later, company X sends me an offer letter (signed). I tell them, "Thanks! Could you please also send the formal contract signed?".

Haven't received a response yet (a few days have passed). I'm not very "trained" in these kind of scenarios, but I won't resign from my current job unless I receive a signed contract by company X, and afaik, an offer letter is not a contract (at least in western europe). What do you think?