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Mirrors > Home > ILE Home > Th. List > rabsnt | Unicode version |
Description: Truth implied by equality of a restricted class abstraction and a singleton. (Contributed by NM, 29-May-2006.) (Proof shortened by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
rabsnt.1 | |
rabsnt.2 |
Ref | Expression |
---|---|
rabsnt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabsnt.1 | . . . 4 | |
2 | 1 | snid 3551 | . . 3 |
3 | id 19 | . . 3 | |
4 | 2, 3 | eleqtrrid 2227 | . 2 |
5 | rabsnt.2 | . . . 4 | |
6 | 5 | elrab 2835 | . . 3 |
7 | 6 | simprbi 273 | . 2 |
8 | 4, 7 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wcel 1480 crab 2418 cvv 2681 csn 3522 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rab 2423 df-v 2683 df-sn 3528 |
This theorem is referenced by: ontr2exmid 4435 onsucsssucexmid 4437 ordsoexmid 4472 unfiexmid 6799 |
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