Metamath Proof Explorer


Theorem renegeu

Description: Existential uniqueness of real negatives. (Contributed by Steven Nguyen, 7-Jan-2023)

Ref Expression
Assertion renegeu ⊢ A ∈ ℝ → ∃! x ∈ ℝ A + x = 0

Proof

Step Hyp Ref Expression
1 id ⊢ A ∈ ℝ → A ∈ ℝ
2 ax-rnegex ⊢ A ∈ ℝ → ∃ x ∈ ℝ A + x = 0
3 1 2 renegeulem ⊢ A ∈ ℝ → ∃! x ∈ ℝ A + x = 0