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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 3153 |
. 2
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2 | elsng 3622 |
. . . 4
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3 | 2 | necon3bbid 2400 |
. . 3
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4 | 3 | pm5.32i 454 |
. 2
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5 | 1, 4 | bitri 184 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-v 2754 df-dif 3146 df-sn 3613 |
This theorem is referenced by: eldifsni 3736 rexdifsn 3739 difsn 3744 fnniniseg2 5660 rexsupp 5661 mpodifsnif 5989 suppssfv 6102 suppssov1 6103 dif1o 6463 fidifsnen 6898 en2eleq 7224 en2other2 7225 elni 7337 divvalap 8661 elnnne0 9220 divfnzn 9651 modfzo0difsn 10426 modsumfzodifsn 10427 hashdifpr 10832 eff2 11720 tanvalap 11748 fzo0dvdseq 11895 oddprmgt2 12166 oddprmdvds 12386 4sqlem19 12441 setsslnid 12564 grpinvnzcl 13016 lssneln0 13690 rplogbval 14823 lgsfcl2 14868 lgsval2lem 14872 lgsval3 14880 lgsmod 14888 lgsdirprm 14896 lgsne0 14900 |
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