DeeDeemensional is the first episode in season one of Dexter's Laboratory, which first aired on April 28, 1996, although it tends to get mixed up with "Dexter's Rival" because this episode was actually the first episode to air on TV, even though "Dexter's Rival" was the first episode to be produced.
In this episode, Dexter has Dee Dee go back in time to tell himself not to open a passage. However, Past Dexter refuses to accept the message, and chaos ensues when Future Dee Dee meets Past Dee Dee.
After a monster comes out of an inter-dimensional doorway that Dexter opens, he quickly writes a note that he gives to Dee Dee, instructing her to go back to the past and give him the note before he opens the passage. Dee Dee turns on the time machine and stands next to it, only for Dexter to tell her she needs to be inside the machine. Dexter in the past doesn't believe Dee Dee, thus he has to do whatever she and Past Dee Dee tells him in order to obtain the message from the future.
This episode was the second produced episode of the series, but it aired first because Cartoon Network often airs episodes out of production order, becoming the series premiere. "Dexter's Rival" was meant to be the series premiere but was held off to the third episode.
This episode is also aired on April 27, 1996 on TNT as a special preview.