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Theorem nfel2 2294
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 2281 . 2  |-  F/_ x A
2 nfeq2.1 . 2  |-  F/_ x B
31, 2nfel 2290 1  |-  F/ x  A  e.  B
Colors of variables: wff set class
Syntax hints:   F/wnf 1436    e. wcel 1480   F/_wnfc 2268
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270
This theorem is referenced by:  elabgt  2825  opelopabsb  4182  eliunxp  4678  opeliunxp2  4679  tz6.12f  5450  0neqopab  5816  disjxp1  6133  opeliunxp2f  6135  cbvixp  6609  ctiunct  11959
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