Admissibility. Any UMP unbiased test 0 is admissible in the sense that there cannot exist another test

Admissibility. Any UMP unbiased test φ0 is admissible in the sense that there cannot exist another test φ1 which is at least as powerful as φ0 against all alternatives and more powerful against some.

[If φ is unbiased and φ is uniformly at least as powerful as φ, then φ is also unbiased.]