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| Mirrors > Home > MPE Home > Th. List > mul02d | Structured version Visualization version GIF version | ||
| Description: Multiplication by 0. Theorem I.6 of [Apostol] p. 18. (Contributed by Mario Carneiro, 27-May-2016.) |
| Ref | Expression |
|---|---|
| muld.1 | ⊢ (𝜑 → 𝐴 ∈ ℂ) |
| Ref | Expression |
|---|---|
| mul02d | ⊢ (𝜑 → (0 · 𝐴) = 0) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | muld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℂ) | |
| 2 | mul02 11439 | . 2 ⊢ (𝐴 ∈ ℂ → (0 · 𝐴) = 0) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (0 · 𝐴) = 0) |
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