Theorem nfel2 2925

Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
nfeq2.1	⊢ Ⅎ𝑥𝐵

Assertion

Ref	Expression
nfel2	⊢ Ⅎ𝑥 𝐴 ∈ 𝐵

Distinct variable group:   𝑥,𝐴

Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem nfel2

Step	Hyp	Ref	Expression
1		nfcv 2907	. 2 ⊢ Ⅎ𝑥𝐴
2		nfeq2.1	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfel 2921	1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵

Syntax hints:  Ⅎwnf 1786   ∈ wcel 2106  Ⅎwnfc 2887

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-nf 1787  df-cleq 2730  df-clel 2816  df-nfc 2889

This theorem is referenced by:  elabgtOLD  3604  elabgOLD  3608  0nelopabOLD  5481  eliunxp  5746  opeliunxp2  5747  tz6.12f  6798  riotaxfrd  7267  opeliunxp2f  8026  cbvixp  8702  boxcutc  8729  ixpiunwdom  9349  rankidb  9558  rankuni2b  9611  acni2  9802  ac6c4  10237  iundom2g  10296  tskuni  10539  reuccatpfxs1  14460  gsumcom2  19576  gsummatr01lem4  21807  ptclsg  22766  cnextfvval  23216  prdsdsf  23520  nnindf  31133  gsumpart  31315  nsgqusf1olem1  31598  nsgqusf1olem3  31600  bnj1463  33035  fineqvrep  33064  ptrest  35776  sdclem1  35901  eqrelf  36395  binomcxplemnotnn0  41974  eliin2f  42654  stoweidlem26  43567  stoweidlem36  43577  stoweidlem46  43587  stoweidlem51  43592  eliunxp2  45669  setrec1  46397