Theorem nfel2 2996

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 2977	. 2 ⊢ Ⅎ𝑥𝐴
2		nfeq2.1	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfel 2992	1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵

Syntax hints:  Ⅎwnf 1780   ∈ wcel 2110  Ⅎwnfc 2961

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781  df-cleq 2814  df-clel 2893  df-nfc 2963

This theorem is referenced by:  elabgt  3662  elabg  3665  opelopabsb  5409  0nelopab  5444  eliunxp  5702  opeliunxp2  5703  tz6.12f  6688  riotaxfrd  7142  opeliunxp2f  7870  cbvixp  8472  boxcutc  8499  ixpiunwdom  9049  rankidb  9223  rankuni2b  9276  acni2  9466  ac6c4  9897  iundom2g  9956  tskuni  10199  reuccatpfxs1  14103  gsumcom2  19089  gsummatr01lem4  21261  ptclsg  22217  cnextfvval  22667  prdsdsf  22971  nnindf  30529  bnj1463  32322  ptrest  34885  sdclem1  35012  eqrelf  35511  binomcxplemnotnn0  40681  eliin2f  41363  stoweidlem26  42305  stoweidlem36  42315  stoweidlem46  42325  stoweidlem51  42330  eliunxp2  44376  setrec1  44788