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Filter using a many-to-many table MySQL

I have the following tables (other tables ommitted for simplicity). 1 is for all of the people, 2 is for the sports that those people play. I am using php to allow a user to see a list of people. They can filter by a person's name, or by the sports they play. So, I want the ability to see all people that play for example baseball and football.

create table people (
  id int,
  name varchar(50)
  );

create table people_to_sports (
  personID int,
  sportID int,
  primary key(personID,sportID)
  );

Basically my question is, how can I use people_to_sports to get a list of all people that play sport 1 and sport 2 for example?

I have a sqlfiddle here .

Thank you!

SELECT
  personID
FROM
  people_to_sports
WHERE
  sportID IN (1, 2)
GROUP BY
  personID
HAVING
  COUNT(*) = 2
SELECT personID, COUNT(personID) AS cnt
FROM people_to_sports
WHERE sportID IN (1, 2)
GROUP BY personID
HAVING cnt = 2

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