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Mirrors > Home > MPE Home > Th. List > negcld | Structured version Visualization version GIF version |
Description: Closure law for negative. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
negidd.1 | ⊢ (𝜑 → 𝐴 ∈ ℂ) |
Ref | Expression |
---|---|
negcld | ⊢ (𝜑 → -𝐴 ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℂ) | |
2 | negcl 11078 | . 2 ⊢ (𝐴 ∈ ℂ → -𝐴 ∈ ℂ) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → -𝐴 ∈ ℂ) |
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