[Python] min from columns from dict

I have a dict with item\column name and a df with columns from dict and other columns. How can I add column to df with min value for every item just from columns corresponding from dict?

import pandas as pd
my_dict={'Item1':['Col1','Col3'],
'Item2':['Col2','Col4']
}
df=pd.DataFrame({
'Col0':['Item1','Item2'],
'Col1':[20,25],
'Col2':[89,15],
'Col3':[26,30],
'Col4':[40,108],
'Col5':[55,2]
})
df['min']=?


I tried

df['min']=df[df.columns[df.columns.isin(my_dict)]].min(axis=1),


but it didn't work.

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