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You know what, you actually mentioned that is within the same DLI so it's my mistake. I assumed that you were transferring from 2 different DLIs. 'Changing majors' is pretty common so as long you did 2 years in the university total, doesn't make a difference.
 
The length of my new program (Bachelor of Science) would only be 3 semesters (unless the duration of the first semester studying under Bachelor of Computer Info Systems counts as well), so that's why I was worried.

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Additional context:

I have already studied for 4 semesters (2 years) at a partner institution in India, so I just need to complete 4 more semesters (2 years) in Canada to get my degree.

The first out of those last 4 semesters (Fall 2020) is already under progress and I'm studying under Bachelor of Computer Info Systems for this semester.

I plan to transfer to Bachelor of Science starting next semester (Winter 2021) - and all of the credits that I earn during the current (Fall 2020) semester are transferrable to the Bachelor of Science program.