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Mirrors > Home > ILE Home > Th. List > nssne2 | Unicode version |
Description: Two classes are different if they are not subclasses of the same class. (Contributed by NM, 23-Apr-2015.) |
Ref | Expression |
---|---|
nssne2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1 2966 | . . . 4 | |
2 | 1 | biimpcd 148 | . . 3 |
3 | 2 | necon3bd 2248 | . 2 |
4 | 3 | imp 115 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wceq 1243 wne 2204 wss 2917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-ne 2206 df-in 2924 df-ss 2931 |
This theorem is referenced by: (None) |
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