Remove lines based on multiple criteria

I am trying to eliminate certain rows in my workbook automatically based on a few fields. The file contains patient encounters with hospitals. Patient can either be discharged from the ED, admitted to inpatient, or discharged from inpatient. If a patient is transferred to inpatient from the ED, it actually comes up in the workbook as an ED Discharge and an Inpatient Admit as two separate rows with the same date. I would like to remove both rows when:

- Patient name is the same
- Date is the same
- Encounter type is ED Discharge and Inpatient Admit

I've attached a sample workbook to illustrate the desired outcome.