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Theorem nfel1 2204
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)
Hypothesis
Ref Expression
nfeq1.1 𝑥𝐴
Assertion
Ref Expression
nfel1 𝑥 𝐴𝐵
Distinct variable group:   𝑥,𝐵
Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfel1
StepHypRef Expression
1 nfeq1.1 . 2 𝑥𝐴
2 nfcv 2194 . 2 𝑥𝐵
31, 2nfel 2202 1 𝑥 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  wnf 1365  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-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-cleq 2049  df-clel 2052  df-nfc 2183
This theorem is referenced by:  vtocl2gf  2632  vtocl3gf  2633  vtoclgaf  2635  vtocl2gaf  2637  vtocl3gaf  2639  nfop  3593  pofun  4077  nfse  4106  rabxfrd  4229  mptfvex  5284  fvmptf  5291  fmptcof  5359  fliftfuns  5466  riota2f  5517  ovmpt2s  5652  ov2gf  5653  fmpt2x  5854  mpt2fvex  5857  qliftfuns  6221
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