Metamath Proof Explorer


Theorem bru2

Description: The basic 2nd root of unity is -u 1 . (Contributed by AV, 24-Oct-2026)

Ref Expression
Assertion bru2 Could not format assertion : No typesetting found for |- ( bRoU ` 2 ) = -u 1 with typecode |-

Proof

Step Hyp Ref Expression
1 2nn ⊢ 2 ∈ ℕ
2 bruval2 Could not format ( 2 e. NN -> ( bRoU ` 2 ) = ( -u 1 ^c ( 2 / 2 ) ) ) : No typesetting found for |- ( 2 e. NN -> ( bRoU ` 2 ) = ( -u 1 ^c ( 2 / 2 ) ) ) with typecode |-
3 1 2 ax-mp Could not format ( bRoU ` 2 ) = ( -u 1 ^c ( 2 / 2 ) ) : No typesetting found for |- ( bRoU ` 2 ) = ( -u 1 ^c ( 2 / 2 ) ) with typecode |-
4 2div2e1 ⊢ 2 2 = 1
5 4 oveq2i ⊢ − 1 2 2 = − 1 1
6 neg1cn ⊢ − 1 ∈ ℂ
7 cxp1 ⊢ − 1 ∈ ℂ → − 1 1 = − 1
8 6 7 ax-mp ⊢ − 1 1 = − 1
9 3 5 8 3eqtri Could not format ( bRoU ` 2 ) = -u 1 : No typesetting found for |- ( bRoU ` 2 ) = -u 1 with typecode |-