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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 11698 | . 2 ⊢ (𝐴 ∈ ℝ → (𝐴 − 1) < 𝐴) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 − 1) < 𝐴) |
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