Theorem nfel2 2361

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 2348	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfel 2357	1 |- F/ x A e. B

Syntax hints:   F/wnf 1483   e. wcel 2176   F/_wnfc 2335

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-cleq 2198  df-clel 2201  df-nfc 2337

This theorem is referenced by:  elabgt  2914  opelopabsb  4306  eliunxp  4817  opeliunxp2  4818  tz6.12f  5605  0neqopab  5990  disjxp1  6322  opeliunxp2f  6324  cbvixp  6802  ctiunct  12811