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Mirrors > Home > ILE Home > Th. List > nelne2 | Unicode version |
Description: Two classes are different if they don't belong to the same class. (Contributed by NM, 25-Jun-2012.) |
Ref | Expression |
---|---|
nelne2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2141 | . . . 4 | |
2 | 1 | biimpcd 157 | . . 3 |
3 | 2 | necon3bd 2288 | . 2 |
4 | 3 | imp 122 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wceq 1284 wcel 1433 wne 2245 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-cleq 2074 df-clel 2077 df-ne 2246 |
This theorem is referenced by: (None) |
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