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Mirrors > Home > ILE Home > Th. List > unssi | Unicode version |
Description: An inference showing the union of two subclasses is a subclass. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
unssi.1 | |
unssi.2 |
Ref | Expression |
---|---|
unssi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unssi.1 | . . 3 | |
2 | unssi.2 | . . 3 | |
3 | 1, 2 | pm3.2i 270 | . 2 |
4 | unss 3281 | . 2 | |
5 | 3, 4 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 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: undifabs 3470 inundifss 3471 dmrnssfld 4849 caserel 7031 ltrelxr 7938 nn0ssre 9094 nn0ssz 9185 strleun 12290 |
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