Theorem nfel2 2363

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 2350	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfel 2359	1 |- F/ x A e. B

Syntax hints:   F/wnf 1484   e. wcel 2178   F/_wnfc 2337

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-cleq 2200  df-clel 2203  df-nfc 2339

This theorem is referenced by:  elabgt  2921  opelopabsb  4324  eliunxp  4835  opeliunxp2  4836  tz6.12f  5628  0neqopab  6013  disjxp1  6345  opeliunxp2f  6347  cbvixp  6825  reuccatpfxs1  11238  ctiunct  12926