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Mirrors > Home > ILE Home > Th. List > onpsssuc | Unicode version |
Description: An ordinal number is a proper subset of its successor. (Contributed by Stefan O'Rear, 18-Nov-2014.) |
Ref | Expression |
---|---|
onpsssuc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elirr 4266 | . . . 4 | |
2 | sucidg 4153 | . . . . 5 | |
3 | eleq2 2101 | . . . . 5 | |
4 | 2, 3 | syl5ibrcom 146 | . . . 4 |
5 | 1, 4 | mtoi 590 | . . 3 |
6 | sssucid 4152 | . . 3 | |
7 | 5, 6 | jctil 295 | . 2 |
8 | dfpss2 3029 | . 2 | |
9 | 7, 8 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wceq 1243 wcel 1393 wss 2917 wpss 2918 con0 4100 csuc 4102 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-setind 4262 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-ral 2311 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pss 2933 df-sn 3381 df-suc 4108 |
This theorem is referenced by: (None) |
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