i caught my man CHEATING?!?

hey everyone! i need advice !

recently ive logged into my bf’s fb (we live together for a year) & found that hes been commenting back & forth w an hnknown account that has no pictures or info but a profile picture of some cartoon ... for the past few days ive seen them replying back & forth in gifs but inappropriately etc ... last night i logged in again & seen she had posted a goodmorning post for everyone & seen my bf in the comments w “goodmorning mami” ..... is this cheating??? like is this worth moving out for? i feel like this is sooo rude especially bc hes always scolding me for “cheating” & having giys on the side but here he is ?????? here are a few screenshots for better understanding.

heres the one of him commenting goodmorning mami & then heres one of the gif convos ...

isnt this disrespectful????? cheating??

it bothers me so much bc i get draggggggged by him often times telling me i have side guys & im cheating / hiding stuff but ive never .. i feel like thats so rude especially living together???

helpppp!!!!

EDIT

I wanna know how to use this as avidence & approach the situation BOLDLY . hes a good manipulator i must admit & will somehow flip this around to me , but i want to be STRONGER . ive found this & kept it a secret for a week now & its weird to pretend were ok bc im looking for “solid proof” hes cheating but u all agree w me that this infact is cheating. would i be wrong in moving out over this?