Theorem nfel2 2231

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 2219	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfel 2227	1 |- F/ x A e. B

Syntax hints:   F/wnf 1389   e. wcel 1433   F/_wnfc 2206

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-cleq 2074  df-clel 2077  df-nfc 2208

This theorem is referenced by:  elabgt  2735  opelopabsb  4015  eliunxp  4493  opeliunxp2  4494  tz6.12f  5223  0neqopab  5570