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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 686 | . . 3 | |
2 | elun 3187 | . . 3 | |
3 | 1, 2 | sylibr 133 | . 2 |
4 | 3 | ssriv 3071 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 682 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: ssun2 3210 ssun3 3211 elun1 3213 inabs 3278 reuun1 3328 un00 3379 undifabs 3409 undifss 3413 snsspr1 3638 snsstp1 3640 snsstp2 3641 prsstp12 3643 exmidundif 4099 sssucid 4307 unexb 4333 dmexg 4773 fvun1 5455 dftpos2 6126 tpostpos2 6130 ac6sfi 6760 caserel 6940 finomni 6980 ressxr 7777 nnssnn0 8948 un0addcl 8978 un0mulcl 8979 nn0ssxnn0 9011 fsumsplit 11144 fsum2d 11172 fsumabs 11202 ennnfonelemss 11850 bdunexb 13045 |
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