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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 3056 | . 2 | |
2 | 19.26 1442 | . . 3 | |
3 | elun 3187 | . . . . . 6 | |
4 | 3 | imbi1i 237 | . . . . 5 |
5 | jaob 684 | . . . . 5 | |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | albii 1431 | . . 3 |
8 | dfss2 3056 | . . . 4 | |
9 | dfss2 3056 | . . . 4 | |
10 | 8, 9 | anbi12i 455 | . . 3 |
11 | 2, 7, 10 | 3bitr4i 211 | . 2 |
12 | 1, 11 | bitr2i 184 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 682 wal 1314 wcel 1465 cun 3039 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-un 3045 df-in 3047 df-ss 3054 |
This theorem is referenced by: unssi 3221 unssd 3222 unssad 3223 unssbd 3224 uneqin 3297 undifss 3413 prss 3646 prssg 3647 tpss 3655 pwundifss 4177 ordsucss 4390 elnn 4489 eqrelrel 4610 xpsspw 4621 relun 4626 relcoi2 5039 dfer2 6398 fimaxre2 10966 uncld 12209 bdeqsuc 13006 exmid1stab 13122 |
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