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Theorem nfeld 2209
 Description: Hypothesis builder for elementhood. (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfeqd.1
nfeqd.2
Assertion
Ref Expression
nfeld

Proof of Theorem nfeld
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-clel 2052 . 2
2 nfv 1437 . . 3
3 nfcvd 2195 . . . . 5
4 nfeqd.1 . . . . 5
53, 4nfeqd 2208 . . . 4
6 nfeqd.2 . . . . 5
76nfcrd 2207 . . . 4
85, 7nfand 1476 . . 3
92, 8nfexd 1660 . 2
101, 9nfxfrd 1380 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wceq 1259  wnf 1365  wex 1397   wcel 1409  wnfc 2181 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-cleq 2049  df-clel 2052  df-nfc 2183 This theorem is referenced by:  nfneld  2322  nfraldxy  2373  nfrexdxy  2374  nfreudxy  2500  nfsbc1d  2802  nfsbcd  2805  sbcrext  2862  nfbrd  3834  nfriotadxy  5503
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