Metamath Proof Explorer


Theorem bj-minftynrr

Description: The extended complex number minfty is not a complex number. (Contributed by BJ, 27-Jun-2019)

Ref Expression
Assertion bj-minftynrr ⊢ ¬ -∞ ∈ ℂ

Proof

Step Hyp Ref Expression
1 df-bj-minfty ⊢ -∞ = inftyexpi ⁡ π
2 bj-inftyexpidisj ⊢ ¬ inftyexpi ⁡ π ∈ ℂ
3 1 2 eqneltri ⊢ ¬ -∞ ∈ ℂ