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Mirrors > Home > MPE Home > Th. List > neeq12i | Structured version Visualization version GIF version |
Description: Inference for inequality. (Contributed by NM, 24-Jul-2012.) (Proof shortened by Wolf Lammen, 25-Nov-2019.) |
Ref | Expression |
---|---|
neeq1i.1 | ⊢ 𝐴 = 𝐵 |
neeq12i.2 | ⊢ 𝐶 = 𝐷 |
Ref | Expression |
---|---|
neeq12i | ⊢ (𝐴 ≠ 𝐶 ↔ 𝐵 ≠ 𝐷) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neeq1i.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
2 | neeq12i.2 | . . 3 ⊢ 𝐶 = 𝐷 | |
3 | 1, 2 | eqeq12i 2756 | . 2 ⊢ (𝐴 = 𝐶 ↔ 𝐵 = 𝐷) |
4 | 3 | necon3bii 2996 | 1 ⊢ (𝐴 ≠ 𝐶 ↔ 𝐵 ≠ 𝐷) |
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