The guy I'm dating doesn't want me to sleep with or date other guys, does that mean we're in a relationship?!

The thing is am dating someone whom I really like. He told me the other day that he doesn't want me to date other guys or sleep with anyone. I told him I don't want the same from him too and if he does find someone else to tell me, and he said he would...so does this mean we're exclusive and in a relationship? I don't wanna ask him or talk about it again...
The guy I'm dating doesn't want me to sleep with or date other guys, does that mean we're in a relationship?!
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