Description: A number equal to its negative is zero. (Contributed by NM, 29-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | divclz.1 | ⊢ 𝐴 ∈ ℂ | |
Assertion | eqnegi | ⊢ ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | ⊢ 𝐴 ∈ ℂ | |
2 | eqneg | ⊢ ( 𝐴 ∈ ℂ → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) |