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Theorem nfel2 2241
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)
Hypothesis
Ref Expression
nfeq2.1  |-  F/_ x B
Assertion
Ref Expression
nfel2  |-  F/ x  A  e.  B
Distinct variable group:    x, A
Allowed substitution hint:    B( x)

Proof of Theorem nfel2
StepHypRef Expression
1 nfcv 2228 . 2  |-  F/_ x A
2 nfeq2.1 . 2  |-  F/_ x B
31, 2nfel 2237 1  |-  F/ x  A  e.  B
Colors of variables: wff set class
Syntax hints:   F/wnf 1394    e. wcel 1438   F/_wnfc 2215
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-cleq 2081  df-clel 2084  df-nfc 2217
This theorem is referenced by:  elabgt  2757  opelopabsb  4087  eliunxp  4575  opeliunxp2  4576  tz6.12f  5333  0neqopab  5694  disjxp1  6001  opeliunxp2f  6003
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