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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 666 |
. . 3
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2 | elun 3114 |
. . 3
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3 | 1, 2 | sylibr 132 |
. 2
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4 | 3 | ssriv 3004 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-v 2604 df-un 2978 df-in 2980 df-ss 2987 |
This theorem is referenced by: ssun2 3137 ssun3 3138 elun1 3140 inabs 3204 reuun1 3253 un00 3297 undifabs 3327 undifss 3330 snsspr1 3541 snsstp1 3543 snsstp2 3544 prsstp12 3546 sssucid 4178 unexb 4203 dmexg 4624 fvun1 5271 dftpos2 5910 tpostpos2 5914 ac6sfi 6431 ressxr 7224 nnssnn0 8358 un0addcl 8388 un0mulcl 8389 nn0ssxnn0 8421 bdunexb 10896 |
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