expression, noun-modifying (irregular)
established; acknowledged; leading
Fixed expression meaning someone or something is so well-established that their status cannot be challenged. Often used prenominally to describe a person, institution, or reputation.
彼は押しも押されもせぬ実力者だ。
He is a fully established person of influence.
この店は押しも押されもせぬ老舗です。
This shop is a long-established and widely recognized store.