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  5416  0nelopab  5451  eliunxp  5707  opeliunxp2  5708  tz6.12f  6693  riotaxfrd  7147  opeliunxp2f  7875  cbvixp  8477  boxcutc  8504  ixpiunwdom  9054  rankidb  9228  rankuni2b  9281  acni2  9471  ac6c4  9902  iundom2g  9961  tskuni  10204  reuccatpfxs1  14108  gsumcom2  19094  gsummatr01lem4  21266  ptclsg  22222  cnextfvval  22672  prdsdsf  22976  nnindf  30534  bnj1463  32327  ptrest  34890  sdclem1  35017  eqrelf  35516  binomcxplemnotnn0  40686  eliin2f  41368  stoweidlem26  42310  stoweidlem36  42320  stoweidlem46  42330  stoweidlem51  42335  eliunxp2  44381  setrec1  44793