my_list = ['1 ab ac bbba','23 abcba a aabb ab','345 ccc ab aaaaa']

I'm trying to get rid of the numbers and the spaces, basically everything that's not an 'a','b', or 'c'

I tried this but it didn't work and I'm not sure why:

for str in my_list:
    for i in str:
        if i != 'a' or 'b' or 'c':
            i = ''
        else:
            pass

I want to eventually get:

my_list2 = ['abacbbba','abcbaaaabbab','cccabaaaaa']