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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 4071 | . . 3 | |
2 | 1 | ralrimivw 2506 | . 2 |
3 | df-se 4255 | . 2 Se | |
4 | 2, 3 | sylibr 133 | 1 Se |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 wral 2416 crab 2420 cvv 2686 class class class wbr 3929 Se wse 4251 |
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 ax-sep 4046 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rab 2425 df-v 2688 df-in 3077 df-ss 3084 df-se 4255 |
This theorem is referenced by: (None) |
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