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Mirrors > Home > ILE Home > Th. List > rabsn | Unicode version |
Description: Condition where a restricted class abstraction is a singleton. (Contributed by NM, 28-May-2006.) |
Ref | Expression |
---|---|
rabsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2203 | . . . . 5 | |
2 | 1 | pm5.32ri 451 | . . . 4 |
3 | 2 | baib 905 | . . 3 |
4 | 3 | abbidv 2258 | . 2 |
5 | df-rab 2426 | . 2 | |
6 | df-sn 3538 | . 2 | |
7 | 4, 5, 6 | 3eqtr4g 2198 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1332 wcel 1481 cab 2126 crab 2421 csn 3532 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-rab 2426 df-sn 3538 |
This theorem is referenced by: unisn3 4374 |
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