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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 2988 | . 2 | |
2 | 19.26 1410 | . . 3 | |
3 | elun 3113 | . . . . . 6 | |
4 | 3 | imbi1i 236 | . . . . 5 |
5 | jaob 663 | . . . . 5 | |
6 | 4, 5 | bitri 182 | . . . 4 |
7 | 6 | albii 1399 | . . 3 |
8 | dfss2 2988 | . . . 4 | |
9 | dfss2 2988 | . . . 4 | |
10 | 8, 9 | anbi12i 447 | . . 3 |
11 | 2, 7, 10 | 3bitr4i 210 | . 2 |
12 | 1, 11 | bitr2i 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wo 661 wal 1282 wcel 1433 cun 2971 wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 |
This theorem is referenced by: unssi 3147 unssd 3148 unssad 3149 unssbd 3150 uneqin 3215 undifss 3323 prss 3541 prssg 3542 tpss 3550 pwundifss 4040 ordsucss 4248 elnn 4346 eqrelrel 4459 xpsspw 4468 relun 4472 relcoi2 4868 dfer2 6130 fimaxre2 10109 bdeqsuc 10672 |
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