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Theorem nfel2 2325
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 2312 . 2  |-  F/_ x A
2 nfeq2.1 . 2  |-  F/_ x B
31, 2nfel 2321 1  |-  F/ x  A  e.  B
Colors of variables: wff set class
Syntax hints:   F/wnf 1453    e. wcel 2141   F/_wnfc 2299
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-cleq 2163  df-clel 2166  df-nfc 2301
This theorem is referenced by:  elabgt  2871  opelopabsb  4243  eliunxp  4748  opeliunxp2  4749  tz6.12f  5523  0neqopab  5896  disjxp1  6213  opeliunxp2f  6215  cbvixp  6690  ctiunct  12384
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