Filter a dataframe with datetime index using another dataframe with date index

I have two dataframes, one dataframe has index with date and time, the other dataframe’s index only has date. Now I’d like to filter rows of first dataframe if its date is within 2nd dataframe’s index.

I can do it but very complicated to use two for loop to check each item. Is there a simple way?

Here is what I did:

First dataframe

import pandas as pd
df=pd.DataFrame({'value':[1,2,3,4,5,6]})
df.index=['2022-01-01 10:00','2022-01-02 13:00','2022-01-07 10:00','2022-01-08 10:00','2022-01-11 10:00','2022-01-12 10:00']
df.index=pd.to_datetime(df.index)
df

    value
2022-01-01 10:00:00 1
2022-01-02 13:00:00 2
2022-01-07 10:00:00 3
2022-01-08 10:00:00 4
2022-01-11 10:00:00 5
2022-01-12 10:00:00 6

2nd dataframe

f_1=pd.DataFrame({'value':[1,2,3]})
df_1.index=['2022-01-02','2022-01-05','2022-01-07']
df_1.index=pd.to_datetime(df_1.index)
df_1

    value
2022-01-02  1
2022-01-05  2
2022-01-07  3

Now I am checking each element of first dataframe’s index is equal to any element of 2nd dataframe’s index. If so, then save value of True

date_same=[False]*len(df.index)
for ix,date1 in enumerate(df.index.date):
    for date2 in df_1.index:
        if date1==date2:
            date_same[ix]=True
            break
date_same   

[False, True, True, False, False, False]

Now using saved list to filter the first dataframe

df_filter=df.loc[date_same]
df_filter

    value
2022-01-02 13:00:00 2
2022-01-07 10:00:00 3