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Mirrors > Home > MPE Home > Th. List > neir | Structured version Visualization version GIF version |
Description: Inference associated with df-ne 2939. (Contributed by BJ, 7-Jul-2018.) |
Ref | Expression |
---|---|
neir.1 | ⊢ ¬ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
neir | ⊢ 𝐴 ≠ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neir.1 | . 2 ⊢ ¬ 𝐴 = 𝐵 | |
2 | df-ne 2939 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
3 | 1, 2 | mpbir 231 | 1 ⊢ 𝐴 ≠ 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 = wceq 1537 ≠ wne 2938 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 207 df-ne 2939 |
This theorem is referenced by: nesymir 2997 vn0 4351 nsuceq0 6469 onnev 6513 nlim2 8527 ax1ne0 11198 ine0 11696 nosgnn0i 27719 1nei 32754 bj-pinftynminfty 37210 |
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