big_league has definitions from the fields of baseball,sport
1
[ noun ] (baseball,sport) the most important league in any sport (especially baseball)

Synonyms

major_league majors

Used in print

(Samuel Elkin, "The Ball Player," Nugget, 6: 5...)

You 're not in the big_leagues , but if you can n't give_and_take down here what the hell do you think it 'll be like up there '' ?

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