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Theorem nfel2 2585
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 2573 . 2  |-  F/_ x A
2 nfeq2.1 . 2  |-  F/_ x B
31, 2nfel 2581 1  |-  F/ x  A  e.  B
Colors of variables: wff set class
Syntax hints:   F/wnf 1554    e. wcel 1726   F/_wnfc 2560
This theorem is referenced by:  elabgt  3080  opelopabsb  4466  eliunxp  5013  opeliunxp2  5014  tz6.12f  5750  0neqopab  6120  riotaxfrd  6582  cbvixp  7080  boxcutc  7106  ixpiunwdom  7560  rankidb  7727  rankuni2b  7780  acni2  7928  ac6c4  8362  iundom2g  8416  tskuni  8659  gsumcom2  15550  ptclsg  17648  cnextfvval  18097  prdsdsf  18398  sdclem1  26448  stoweidlem26  27752  stoweidlem36  27762  stoweidlem46  27772  stoweidlem51  27777  bnj1463  29425
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2430  df-clel 2433  df-nfc 2562
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