From wikipedia about If-magazine:
If was an American science fiction magazine launched in March 1952 by Quinn Publications, owned by James L. Quinn.
The magazine was moderately successful, though it was never regarded as one of the first rank of science fiction magazines. It achieved its greatest success under editor Frederik Pohl, winning the Hugo Award for best professional magazine three years running from 1966 to 1968. If published many award-winning stories over its 22 years, including Robert A. Heinlein's novel The Moon Is a Harsh Mistress, and Harlan Ellison's short story "I Have No Mouth and I Must Scream". Several well-known writers sold their first story to If; the most successful was Larry Niven, whose story "The Coldest Place" appeared in the December 1964 issue.
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