the big leagues

: of great strength

: of great force

: large or great in dimensions, bulk, or extent

: in a loud or declamatory manner

: to a large amount or extent

: on a large scale

: an individual or organization of outstanding importance or power

: a big player : a center or forward whose large size and strength are used to control play near the basket

: any of various units of distance from about 2.4 to 4.6 statute miles (3.9 to 7.4 kilometers)

: a square league

: an association of nations or other political entities for a common purpose

: an association of persons or groups united by common interests or goals

: a group of sports teams that regularly play one another

: to unite in a league

: to form a league