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Mirrors > Home > ILE Home > Th. List > eldifsn | Unicode version |
Description: Membership in a set with an element removed. (Contributed by NM, 10-Oct-2007.) |
Ref | Expression |
---|---|
eldifsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3050 | . 2 | |
2 | elsng 3512 | . . . 4 | |
3 | 2 | necon3bbid 2325 | . . 3 |
4 | 3 | pm5.32i 449 | . 2 |
5 | 1, 4 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wcel 1465 wne 2285 cdif 3038 csn 3497 |
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-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-v 2662 df-dif 3043 df-sn 3503 |
This theorem is referenced by: eldifsni 3622 rexdifsn 3625 difsn 3627 fnniniseg2 5511 rexsupp 5512 mpodifsnif 5832 suppssfv 5946 suppssov1 5947 dif1o 6303 fidifsnen 6732 en2eleq 7019 en2other2 7020 elni 7084 divvalap 8402 elnnne0 8959 divfnzn 9381 modfzo0difsn 10136 modsumfzodifsn 10137 hashdifpr 10534 eff2 11313 tanvalap 11342 fzo0dvdseq 11482 oddprmgt2 11741 setsslnid 11937 |
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