Python[pandas]: Select certain rows by index of another dataframe

Use isin:

df = df[df.index.isin(df1.index)]

Or get all intersectioned indices and select by loc:

df = df.loc[df.index & df1.index]
df = df.loc[np.intersect1d(df.index, df1.index)]
df = df.loc[df.index.intersection(df1.index)]

print (df)
    A  B  C  D
1   1  4  9  1
3   5  5  1  0
22  1  3  9  6

EDIT:

I tried solution: df = df.loc[df1.index]. Do you think that this solution is correct?

Solution is incorrect:

df = df.loc[df1.index]
print (df)

      A    B    C    D
1   1.0  4.0  9.0  1.0
3   5.0  5.0  1.0  0.0
4   NaN  NaN  NaN  NaN
5   NaN  NaN  NaN  NaN
6   NaN  NaN  NaN  NaN
7   NaN  NaN  NaN  NaN
22  1.0  3.0  9.0  6.0
28  NaN  NaN  NaN  NaN
29  NaN  NaN  NaN  NaN
32  NaN  NaN  NaN  NaN
C:/Dropbox/work-joy/so/_t/t.py:23: FutureWarning: 
Passing list-likes to .loc or [] with any missing label will raise
KeyError in the future, you can use .reindex() as an alternative.

See the documentation here:
http://pandas.pydata.org/pandas-docs/stable/indexing.html#deprecate-loc-reindex-listlike
  print (df)