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Mirrors > Home > MPE Home > Th. List > gtneii | Structured version Visualization version GIF version |
Description: 'Less than' implies not equal. (Contributed by Mario Carneiro, 30-Sep-2013.) |
Ref | Expression |
---|---|
lt.1 | ⊢ 𝐴 ∈ ℝ |
ltneii.2 | ⊢ 𝐴 < 𝐵 |
Ref | Expression |
---|---|
gtneii | ⊢ 𝐵 ≠ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt.1 | . 2 ⊢ 𝐴 ∈ ℝ | |
2 | ltneii.2 | . 2 ⊢ 𝐴 < 𝐵 | |
3 | ltne 10929 | . 2 ⊢ ((𝐴 ∈ ℝ ∧ 𝐴 < 𝐵) → 𝐵 ≠ 𝐴) | |
4 | 1, 2, 3 | mp2an 692 | 1 ⊢ 𝐵 ≠ 𝐴 |
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