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Metamath Proof Explorer

Theorem negne0i

Description: The negative of a nonzero number is nonzero. (Contributed by NM, 30-Jul-2004)

Ref Expression
Hypotheses negidi.1 ⊢ A ∈ ℂ
negne0i.2 ⊢ A ≠ 0
Assertion negne0i ⊢ − A ≠ 0

Proof

Step Hyp Ref Expression
1 negidi.1 ⊢ A ∈ ℂ
2 negne0i.2 ⊢ A ≠ 0
3 1 negne0bi ⊢ A ≠ 0 ↔ − A ≠ 0
4 2 3 mpbi ⊢ − A ≠ 0