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Mirrors > Home > MPE Home > Th. List > neneqd | Structured version Visualization version GIF version |
Description: Deduction eliminating inequality definition. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
neneqd.1 | ⊢ (𝜑 → 𝐴 ≠ 𝐵) |
Ref | Expression |
---|---|
neneqd | ⊢ (𝜑 → ¬ 𝐴 = 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neneqd.1 | . 2 ⊢ (𝜑 → 𝐴 ≠ 𝐵) | |
2 | df-ne 2941 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
3 | 1, 2 | sylib 221 | 1 ⊢ (𝜑 → ¬ 𝐴 = 𝐵) |
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