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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 2423 | . . 3 | |
2 | sniota 5115 | . . 3 | |
3 | 1, 2 | sylbi 120 | . 2 |
4 | df-rab 2425 | . 2 | |
5 | df-riota 5730 | . . 3 | |
6 | 5 | sneqi 3539 | . 2 |
7 | 3, 4, 6 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 weu 1999 cab 2125 wreu 2418 crab 2420 csn 3527 cio 5086 crio 5729 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-un 3075 df-sn 3533 df-pr 3534 df-uni 3737 df-iota 5088 df-riota 5730 |
This theorem is referenced by: divalgmod 11624 |
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