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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 2180 | . . . 4 | |
2 | 1 | biimpcd 158 | . . 3 |
3 | 2 | necon3bd 2328 | . 2 |
4 | 3 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1316 wcel 1465 wne 2285 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 df-ne 2286 |
This theorem is referenced by: nelelne 2377 elnelne2 2390 |
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