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Theorem nfel 2288
 Description: Hypothesis builder for elementhood. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfnfc.1
nfeq.2
Assertion
Ref Expression
nfel

Proof of Theorem nfel
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-clel 2133 . 2
2 nfcv 2279 . . . . 5
3 nfnfc.1 . . . . 5
42, 3nfeq 2287 . . . 4
5 nfeq.2 . . . . 5
65nfcri 2273 . . . 4
74, 6nfan 1544 . . 3
87nfex 1616 . 2
91, 8nfxfr 1450 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1331  wnf 1436  wex 1468   wcel 1480  wnfc 2266 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2130  df-clel 2133  df-nfc 2268 This theorem is referenced by:  nfel1  2290  nfel2  2292  nfnel  2408  elabgf  2821  elrabf  2833  sbcel12g  3012  nfdisjv  3913  rabxfrd  4385  ffnfvf  5572  mptelixpg  6621  elabgft1  12974  elabgf2  12976  bj-rspgt  12982
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