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Theorem nfel2 2206
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 2194 . 2 𝑥𝐴
2 nfeq2.1 . 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:  elabgt  2707  opelopabsb  4025  eliunxp  4503  opeliunxp2  4504  tz6.12f  5230  0neqopab  5578
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