MySQL 8.0

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

CREATE TABLE user_private_message (
  id INT NOT NULL AUTO_INCREMENT PRIMARY KEY,
  user_from_id INT NOT NULL,
  send_time TIMESTAMP NOT NULL DEFAULT NOW()
);
INSERT INTO user_private_message(user_from_id, send_time)
VALUES
  (1, '2007-01-01 00:00:00'),
  (1, '2007-01-02 00:00:00'),
  (2, '2007-01-02 00:00:00'),
  (3, '2007-01-02 00:00:00'),
  (1, '2007-01-03 00:00:00'),
  (2, '2007-01-03 00:00:00'),
  (3, '2007-01-03 00:00:00'),
  (1, '2007-01-04 00:00:00'),
  (2, '2007-01-04 00:00:00'),
  (3, '2007-01-04 00:00:00'),
  (1, '2007-01-05 00:00:00'),
  (2, '2007-01-05 00:00:00');

Records: 12  Duplicates: 0  Warnings: 0


SELECT DISTINCT DATE(send_time)
FROM user_private_message
GROUP BY DATE(send_time), user_from_id
HAVING COUNT(user_from_id) = 1;


DATE(send_time)


2007-01-01

2007-01-02

2007-01-03

2007-01-04

2007-01-05