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Mirrors > Home > ILE Home > Th. List > ssnelpss | Unicode version |
Description: A subclass missing a member is a proper subclass. (Contributed by NM, 12-Jan-2002.) |
Ref | Expression |
---|---|
ssnelpss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nelneq2 2139 | . . 3 | |
2 | eqcom 2042 | . . 3 | |
3 | 1, 2 | sylnib 601 | . 2 |
4 | dfpss2 3029 | . . 3 | |
5 | 4 | baibr 829 | . 2 |
6 | 3, 5 | syl5ib 143 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wceq 1243 wcel 1393 wss 2917 wpss 2918 |
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-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 df-ne 2206 df-pss 2933 |
This theorem is referenced by: ssnelpssd 3290 |
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