Description: A complex number equals its negative iff it is zero. Deduction form of eqneg . (Contributed by David Moews, 28-Feb-2017)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eqnegd.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
Assertion | eqnegd | ⊢ ( 𝜑 → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqnegd.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
2 | eqneg | ⊢ ( 𝐴 ∈ ℂ → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) ) |