Python produce True False output after comparing two indexes from different dataframes using one line code

I have two data frames as given below

small_df =

index    data1
2         123
3         436

big_df =

index    data1
0          78
1          67
2          13
3          46

I want to compare check if any index of small_df present in big_df using a one line code and produce True or False. My code:

 big_idx  = [True for i in small_df.index if i in big_df.index]

My present output

big_idx = [True True]

My expected output

big_idx = [False False True True]

How to insert False in my code? I tried following code but not successful.

[True for i in small_df.index if i in big_df.index else False]