What is the syntax of a double for loop into a list comprehension with if and else statement in the first for loop?

I was wondering what would be the syntax of a double for loop into a list comprehension which have an if and else statement used in the first for loop. So this question born from this function that I made, where I have one list comprehension with two loops but the if and else statements are in the second loop:

def double_for_list_comp_ifelse_second_loop(lst):
    return [(j if j == 1 else 0)  for i in lst for j in i]


l = [[0,1],[0,3]]
double_for_list_comp_ifelse_second_loop(lst=l)

output: [0, 1, 0, 0]

The list comprehension should compress this syntax:

for i in lst:
    if...
    else...
    for j in i:
      if...
      else...