Theorem nfeq2 2362

Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
nfeq2.1	|- F/_ x B

Assertion

Ref	Expression
nfeq2	|- F/ x A = B

Distinct variable group:   x, A

Allowed substitution hint:   B( x)

Proof of Theorem nfeq2

Step	Hyp	Ref	Expression
1		nfcv 2350	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfeq 2358	1 |- F/ x A = B

Syntax hints:   = wceq 1373   F/wnf 1484   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:  issetf  2784  eqvincf  2905  csbhypf  3140  nfpr  3693  intab  3928  nfmpt  4152  cbvmptf  4154  cbvmpt  4155  repizf2  4222  moop2  4314  eusvnf  4518  elrnmpt1  4948  iotaexab  5269  fmptco  5769  elabrex  5849  elabrexg  5850  nfmpo  6037  cbvmpox  6046  ovmpodxf  6094  fmpox  6309  f1od2  6344  nfrecs  6416  erovlem  6737  xpf1o  6966  mapxpen  6970  mkvprop  7286  cc3  7415  lble  9055  nfsum1  11782  nfsum  11783  zsumdc  11810  fsum3  11813  fsum3cvg2  11820  fsum2dlemstep  11860  mertenslem2  11962  nfcprod1  11980  nfcprod  11981  zproddc  12005  fprod2dlemstep  12048  ctiunctlemfo  12925  ellimc3apf  15247