Theorem nfel2 2385

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

Step	Hyp	Ref	Expression
1		nfcv 2372	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfel 2381	1 |- F/ x A e. B

Syntax hints:   F/wnf 1506   e. wcel 2200   F/_wnfc 2359

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-cleq 2222  df-clel 2225  df-nfc 2361

This theorem is referenced by:  elabgt  2944  opelopabsb  4348  eliunxp  4861  opeliunxp2  4862  tz6.12f  5656  0neqopab  6049  disjxp1  6382  opeliunxp2f  6384  cbvixp  6862  reuccatpfxs1  11279  ctiunct  13011