Description: Negative is one-to-one. (Contributed by NM, 1-Aug-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negidi.1 | ⊢ 𝐴 ∈ ℂ | |
pncan3i.2 | ⊢ 𝐵 ∈ ℂ | ||
Assertion | neg11i | ⊢ ( - 𝐴 = - 𝐵 ↔ 𝐴 = 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidi.1 | ⊢ 𝐴 ∈ ℂ | |
2 | pncan3i.2 | ⊢ 𝐵 ∈ ℂ | |
3 | neg11 | ⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( - 𝐴 = - 𝐵 ↔ 𝐴 = 𝐵 ) ) | |
4 | 1 2 3 | mp2an | ⊢ ( - 𝐴 = - 𝐵 ↔ 𝐴 = 𝐵 ) |