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Theorem nfel 2238
 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 2085 . 2
2 nfcv 2229 . . . . 5
3 nfnfc.1 . . . . 5
42, 3nfeq 2237 . . . 4
5 nfeq.2 . . . . 5
65nfcri 2223 . . . 4
74, 6nfan 1503 . . 3
87nfex 1574 . 2
91, 8nfxfr 1409 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1290  wnf 1395  wex 1427   wcel 1439  wnfc 2216 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-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-cleq 2082  df-clel 2085  df-nfc 2218 This theorem is referenced by:  nfel1  2240  nfel2  2242  nfnel  2358  elabgf  2759  elrabf  2770  sbcel12g  2947  nfdisjv  3840  rabxfrd  4304  ffnfvf  5471  mptelixpg  6505  elabgft1  11951  elabgf2  11953  bj-rspgt  11959
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