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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 702 |
. . 3
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2 | elun 3222 |
. . 3
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3 | 1, 2 | sylibr 133 |
. 2
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4 | 3 | ssriv 3106 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 |
This theorem is referenced by: ssun2 3245 ssun3 3246 elun1 3248 inabs 3313 reuun1 3363 un00 3414 undifabs 3444 undifss 3448 snsspr1 3676 snsstp1 3678 snsstp2 3679 prsstp12 3681 exmidundif 4137 sssucid 4345 unexb 4371 dmexg 4811 fvun1 5495 dftpos2 6166 tpostpos2 6170 ac6sfi 6800 caserel 6980 finomni 7020 ressxr 7833 nnssnn0 9004 un0addcl 9034 un0mulcl 9035 nn0ssxnn0 9067 fsumsplit 11208 fsum2d 11236 fsumabs 11266 ennnfonelemss 11959 bdunexb 13289 |
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