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Theorem nfel2 2187
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 A B
Distinct variable group:   x,A
Allowed substitution hint:   B(x)

Proof of Theorem nfel2
StepHypRef Expression
1 nfcv 2175 . 2 xA
2 nfeq2.1 . 2 xB
31, 2nfel 2183 1 x A B
Colors of variables: wff set class
Syntax hints:  wnf 1346   wcel 1390  wnfc 2162
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164
This theorem is referenced by:  elabgt  2678  opelopabsb  3988  eliunxp  4418  opeliunxp2  4419  tz6.12f  5145  0neqopab  5492
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