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Mirrors > Home > ILE Home > Th. List > snriota | Unicode version |
Description: A restricted class abstraction with a unique member can be expressed as a singleton. (Contributed by NM, 30-May-2006.) |
Ref | Expression |
---|---|
snriota |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-reu 2455 | . . 3 | |
2 | sniota 5189 | . . 3 | |
3 | 1, 2 | sylbi 120 | . 2 |
4 | df-rab 2457 | . 2 | |
5 | df-riota 5809 | . . 3 | |
6 | 5 | sneqi 3595 | . 2 |
7 | 3, 4, 6 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 weu 2019 wcel 2141 cab 2156 wreu 2450 crab 2452 csn 3583 cio 5158 crio 5808 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-reu 2455 df-rab 2457 df-v 2732 df-sbc 2956 df-un 3125 df-sn 3589 df-pr 3590 df-uni 3797 df-iota 5160 df-riota 5809 |
This theorem is referenced by: divalgmod 11886 |
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