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| Mirrors > Home > MPE Home > Th. List > mullidd | Structured version Visualization version GIF version | ||
| Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016.) |
| Ref | Expression |
|---|---|
| addcld.1 | ⊢ (𝜑 → 𝐴 ∈ ℂ) |
| Ref | Expression |
|---|---|
| mullidd | ⊢ (𝜑 → (1 · 𝐴) = 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | addcld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℂ) | |
| 2 | mullid 11260 | . 2 ⊢ (𝐴 ∈ ℂ → (1 · 𝐴) = 𝐴) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (1 · 𝐴) = 𝐴) |
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