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| Mirrors > Home > MPE Home > Th. List > ltm1d | Structured version Visualization version GIF version | ||
| Description: A number minus 1 is less than itself. (Contributed by Mario Carneiro, 28-May-2016.) |
| Ref | Expression |
|---|---|
| ltp1d.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
| Ref | Expression |
|---|---|
| ltm1d | ⊢ (𝜑 → (𝐴 − 1) < 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ltp1d.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
| 2 | ltm1 12109 | . 2 ⊢ (𝐴 ∈ ℝ → (𝐴 − 1) < 𝐴) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 − 1) < 𝐴) |
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