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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 2449 | . . 3 | |
2 | sniota 5174 | . . 3 | |
3 | 1, 2 | sylbi 120 | . 2 |
4 | df-rab 2451 | . 2 | |
5 | df-riota 5792 | . . 3 | |
6 | 5 | sneqi 3582 | . 2 |
7 | 3, 4, 6 | 3eqtr4g 2222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 weu 2013 wcel 2135 cab 2150 wreu 2444 crab 2446 csn 3570 cio 5145 crio 5791 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-un 3115 df-sn 3576 df-pr 3577 df-uni 3784 df-iota 5147 df-riota 5792 |
This theorem is referenced by: divalgmod 11849 |
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