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Theorem eldifsn 3495
 Description: Membership in a set with an element removed. (Contributed by NM, 10-Oct-2007.)
Assertion
Ref Expression
eldifsn

Proof of Theorem eldifsn
StepHypRef Expression
1 eldif 2927 . 2
2 elsng 3390 . . . 4
32necon3bbid 2245 . . 3
43pm5.32i 427 . 2
51, 4bitri 173 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 97   wb 98   wcel 1393   wne 2204   cdif 2914  csn 3375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-v 2559  df-dif 2920  df-sn 3381 This theorem is referenced by:  eldifsni  3496  rexdifsn  3499  difsn  3501  fnniniseg2  5290  rexsupp  5291  suppssfv  5708  suppssov1  5709  dif1o  6021  fidifsnen  6331  elni  6406  divvalap  7653  elnnne0  8195  divfnzn  8556
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