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db<>fiddle
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CREATE TABLE UserPermissions( user VARCHAR(89), permission VARCHAR(89) );

INSERT INTO UserPermissions VALUES
('user1','permission1'),
('user1','permission1'),
('user1','permission2'),
('user2','permission1'),
('user2','permission1'),
('user3','permission1'),
('user3','permission3'),
('user4','permission1');

SELECT user
FROM UserPermissions
GROUP BY user
HAVING COUNT(*) = SUM(CASE WHEN permission = 'permission1' THEN 1 END)
user
user2
user4