Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2715 | . . . 4 | |
2 | elecg 6518 | . . . 4 | |
3 | 1, 2 | mpan 421 | . . 3 |
4 | brcnvg 4767 | . . . 4 | |
5 | 1, 4 | mpan2 422 | . . 3 |
6 | epelg 4250 | . . 3 | |
7 | 3, 5, 6 | 3bitrd 213 | . 2 |
8 | 7 | eqrdv 2155 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wcel 2128 cvv 2712 class class class wbr 3965 cep 4247 ccnv 4585 cec 6478 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-eprel 4249 df-xp 4592 df-cnv 4594 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 df-ec 6482 |
This theorem is referenced by: addcnsrec 7762 mulcnsrec 7763 |
Copyright terms: Public domain | W3C validator |