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Theorem nfel2 2248
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)
Hypothesis
Ref Expression
nfeq2.1 𝑥𝐵
Assertion
Ref Expression
nfel2 𝑥 𝐴𝐵
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem nfel2
StepHypRef Expression
1 nfcv 2235 . 2 𝑥𝐴
2 nfeq2.1 . 2 𝑥𝐵
31, 2nfel 2244 1 𝑥 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  wnf 1401  wcel 1445  wnfc 2222
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 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-cleq 2088  df-clel 2091  df-nfc 2224
This theorem is referenced by:  elabgt  2771  opelopabsb  4111  eliunxp  4606  opeliunxp2  4607  tz6.12f  5368  0neqopab  5732  disjxp1  6039  opeliunxp2f  6041  cbvixp  6512
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