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Mirrors > Home > ILE Home > Th. List > ssin | Unicode version |
Description: Subclass of intersection. Theorem 2.8(vii) of [Monk1] p. 26. (Contributed by NM, 15-Jun-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ssin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3229 | . . . . 5 | |
2 | 1 | imbi2i 225 | . . . 4 |
3 | 2 | albii 1431 | . . 3 |
4 | jcab 577 | . . . 4 | |
5 | 4 | albii 1431 | . . 3 |
6 | 19.26 1442 | . . 3 | |
7 | 3, 5, 6 | 3bitrri 206 | . 2 |
8 | dfss2 3056 | . . 3 | |
9 | dfss2 3056 | . . 3 | |
10 | 8, 9 | anbi12i 455 | . 2 |
11 | dfss2 3056 | . 2 | |
12 | 7, 10, 11 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wcel 1465 cin 3040 wss 3041 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 |
This theorem is referenced by: ssini 3269 ssind 3270 uneqin 3297 trin 4006 pwin 4174 peano5 4482 fin 5279 tgval 12145 eltg3i 12152 innei 12259 cnptoprest2 12336 |
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