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Mirrors > Home > ILE Home > Th. List > ecidg | Unicode version |
Description: A set is equal to its converse epsilon coset. (Note: converse epsilon is not an equivalence relation.) (Contributed by Jim Kingdon, 8-Jan-2020.) |
Ref | Expression |
---|---|
ecidg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2733 | . . . 4 | |
2 | elecg 6551 | . . . 4 | |
3 | 1, 2 | mpan 422 | . . 3 |
4 | brcnvg 4792 | . . . 4 | |
5 | 1, 4 | mpan2 423 | . . 3 |
6 | epelg 4275 | . . 3 | |
7 | 3, 5, 6 | 3bitrd 213 | . 2 |
8 | 7 | eqrdv 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 wcel 2141 cvv 2730 class class class wbr 3989 cep 4272 ccnv 4610 cec 6511 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-eprel 4274 df-xp 4617 df-cnv 4619 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 df-ec 6515 |
This theorem is referenced by: addcnsrec 7804 mulcnsrec 7805 |
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