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Mirrors > Home > ILE Home > Th. List > unss | Unicode version |
Description: The union of two subclasses is a subclass. Theorem 27 of [Suppes] p. 27 and its converse. (Contributed by NM, 11-Jun-2004.) |
Ref | Expression |
---|---|
unss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 2934 | . 2 | |
2 | 19.26 1370 | . . 3 | |
3 | elun 3084 | . . . . . 6 | |
4 | 3 | imbi1i 227 | . . . . 5 |
5 | jaob 631 | . . . . 5 | |
6 | 4, 5 | bitri 173 | . . . 4 |
7 | 6 | albii 1359 | . . 3 |
8 | dfss2 2934 | . . . 4 | |
9 | dfss2 2934 | . . . 4 | |
10 | 8, 9 | anbi12i 433 | . . 3 |
11 | 2, 7, 10 | 3bitr4i 201 | . 2 |
12 | 1, 11 | bitr2i 174 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wo 629 wal 1241 wcel 1393 cun 2915 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-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 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 |
This theorem is referenced by: unssi 3118 unssd 3119 unssad 3120 unssbd 3121 nsspssun 3170 uneqin 3188 undifss 3303 prss 3520 prssg 3521 tpss 3529 pwundifss 4022 ordsucss 4230 elnn 4328 eqrelrel 4441 xpsspw 4450 relun 4454 relcoi2 4848 dfer2 6107 bdeqsuc 10001 |
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