Filter the data-frame by old date and Name R

Question

I have multiple records for each patient but I want to keep the old records of different drugs by Date. Suppose patient AB1 has drug ABC on 1st of July and then the same drug on 5th of July, so I want to keep the date of 1st July and delete the rest repating drugs at different dates. Below is the example of target and resultant data frame.

   Pat_ID       Date      Code      Drug_Names
    AB1     2010-12-09     1.1.1     Alpha
    AB1     2010-12-15     1.1.1     Alpha
    AB1     2010-12-15     1.1.1     Beta
    Ax2     2010-12-09     1.1.1     Beta
    Ax2     2010-12-17     1.1.1     Beta
    Aq3     2011-02-09     1.1.1     Gamma
    Aq3     2011-04-25     1.1.1     Gamma
    Aw4     2011-04-25     1.1.1     Tango

Resultant Dataframe below.

Pat_ID   Date        Code     Drug_Names
AB1     2010-12-09     1.1.1     Alpha
AB1     2010-12-15     1.1.1     Beta
Ax2     2010-12-09     1.1.1     Beta
Aq3     2011-02-09     1.1.1     Gamma
Aw4     2011-04-25     1.1.1     Tango