Theorem nfel2 2949

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 2931	. 2 ⊢ Ⅎ𝑥𝐴
2		nfeq2.1	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfel 2945	1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵

Syntax hints:  Ⅎwnf 1810   ∈ wcel 2149  Ⅎwnfc 2916

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-10 2182  ax-11 2198  ax-12 2219  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1570  df-ex 1807  df-nf 1811  df-cleq 2761  df-clel 2844  df-nfc 2918

This theorem is referenced by:  eliunxp  5821  opeliunxp2  5822  tz6.12f  6904  riotaxfrd  7399  opeliunxp2f  8202  cbvixp  8908  boxcutc  8935  ixpiunwdom  9548  rankidb  9768  rankuni2b  9821  acni2  10026  ac6c4  10461  iundom2g  10520  tskuni  10764  reuccatpfxs1  14780  gsumcom2  20041  gsummatr01lem4  22780  ptclsg  23737  cnextfvval  24187  prdsdsf  24489  nnindf  33101  gsumpart  33320  nsgqusf1olem1  33662  nsgqusf1olem3  33664  bnj1463  35384  fineqvrep  35446  ptrest  38153  sdclem1  38277  eqrelf  38792  binomcxplemnotnn0  44953  eliin2f  45709  stoweidlem26  46627  stoweidlem36  46637  stoweidlem46  46647  stoweidlem51  46652  sge0f1o  46983  finfdm  47447  eliunxp2  48994  setrec1  50349