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| Description: Distribution of negative over subtraction. (Contributed by Mario Carneiro, 27-May-2016.) | 
| Ref | Expression | 
|---|---|
| negidd.1 | ⊢ (𝜑 → 𝐴 ∈ ℂ) | 
| pncand.2 | ⊢ (𝜑 → 𝐵 ∈ ℂ) | 
| Ref | Expression | 
|---|---|
| negsubdi2d | ⊢ (𝜑 → -(𝐴 − 𝐵) = (𝐵 − 𝐴)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | negidd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℂ) | |
| 2 | pncand.2 | . 2 ⊢ (𝜑 → 𝐵 ∈ ℂ) | |
| 3 | negsubdi2 11568 | . 2 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → -(𝐴 − 𝐵) = (𝐵 − 𝐴)) | |
| 4 | 1, 2, 3 | syl2anc 584 | 1 ⊢ (𝜑 → -(𝐴 − 𝐵) = (𝐵 − 𝐴)) | 
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