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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3009 |
. 2
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2 | elsng 3465 |
. . . 4
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3 | 2 | necon3bbid 2296 |
. . 3
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4 | 3 | pm5.32i 443 |
. 2
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5 | 1, 4 | bitri 183 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-v 2622 df-dif 3002 df-sn 3456 |
This theorem is referenced by: eldifsni 3575 rexdifsn 3578 difsn 3580 fnniniseg2 5436 rexsupp 5437 suppssfv 5866 suppssov1 5867 dif1o 6216 fidifsnen 6640 en2eleq 6882 en2other2 6883 elni 6928 divvalap 8202 elnnne0 8748 divfnzn 9167 modfzo0difsn 9863 modsumfzodifsn 9864 hashdifpr 10289 eff2 11031 tanvalap 11060 fzo0dvdseq 11197 oddprmgt2 11454 setsslnid 11606 |
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