noun
a professional sports league or a high level of competition or achievement
adjective
of or relating to a high level of competition or achievement
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The company's recent acquisition has propelled them into the big league of competitors.
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After signing with a major record label, she knew she was in the big league now.
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He's been playing so well, he's definitely in the big league now.
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Making it to the final round of the competition put her in the big league of talented performers.