Postgres 13

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create table Patients (Patient varchar(50), Doctor_Date date, Nurse_Date date, Physio_Date date);

CREATE TABLE

insert into Patients (Patient,Doctor_Date)values ('Patient 1','26/11/2021');
insert into Patients (Patient,Doctor_Date,Nurse_Date,Physio_Date) values('Patient 2','17/11/2021','20/11/2021','16/11/2021');
insert into Patients (Patient,Nurse_Date,Physio_Date) values('Patient 3','5/12/2021','4/05/2021');

INSERT 0 1

INSERT 0 1

INSERT 0 1

 select Patient, 
             (SELECT MIN(mindate) FROM (VALUES (Doctor_Date), (Nurse_Date), (Physio_Date)) AS X(mindate)) AS Minimum_Date
 from Patients             

patient
minimum_date

Patient 1
2021-11-26

Patient 2
2021-11-16

Patient 3
2021-05-04

SELECT 3