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Mirrors > Home > ILE Home > Th. List > ssun1 | Unicode version |
Description: Subclass relationship for union of classes. Theorem 25 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
ssun1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 702 | . . 3 | |
2 | elun 3249 | . . 3 | |
3 | 1, 2 | sylibr 133 | . 2 |
4 | 3 | ssriv 3132 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 698 wcel 2128 cun 3100 wss 3102 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 |
This theorem is referenced by: ssun2 3272 ssun3 3273 elun1 3275 inabs 3340 reuun1 3390 un00 3441 undifabs 3471 undifss 3475 snsspr1 3706 snsstp1 3708 snsstp2 3709 prsstp12 3711 exmidundif 4169 sssucid 4377 unexb 4404 dmexg 4852 fvun1 5536 dftpos2 6210 tpostpos2 6214 ac6sfi 6845 caserel 7033 finomni 7085 ressxr 7923 nnssnn0 9098 un0addcl 9128 un0mulcl 9129 nn0ssxnn0 9161 fsumsplit 11315 fsum2d 11343 fsumabs 11373 fprodsplitdc 11504 fprod2d 11531 ennnfonelemss 12209 bdunexb 13566 |
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