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Mirrors > Home > ILE Home > Th. List > exse | Unicode version |
Description: Any relation on a set is set-like on it. (Contributed by Mario Carneiro, 22-Jun-2015.) |
Ref | Expression |
---|---|
exse | Se |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabexg 3921 | . . 3 | |
2 | 1 | ralrimivw 2435 | . 2 |
3 | df-se 4088 | . 2 Se | |
4 | 2, 3 | sylibr 132 | 1 Se |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 wral 2348 crab 2352 cvv 2601 class class class wbr 3785 Se wse 4084 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rab 2357 df-v 2603 df-in 2979 df-ss 2986 df-se 4088 |
This theorem is referenced by: (None) |
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