Theorem nfeq2 2384

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 2372	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfeq 2380	1 |- F/ x A = B

Syntax hints:   = wceq 1395   F/wnf 1506   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:  issetf  2807  eqvincf  2928  csbhypf  3163  nfpr  3716  intab  3952  nfmpt  4176  cbvmptf  4178  cbvmpt  4179  repizf2  4246  moop2  4338  eusvnf  4544  elrnmpt1  4975  iotaexab  5297  fmptco  5803  elabrex  5887  elabrexg  5888  nfmpo  6079  cbvmpox  6088  ovmpodxf  6136  fmpox  6352  f1od2  6387  nfrecs  6459  erovlem  6782  xpf1o  7013  mapxpen  7017  mkvprop  7336  cc3  7465  lble  9105  nfsum1  11883  nfsum  11884  zsumdc  11911  fsum3  11914  fsum3cvg2  11921  fsum2dlemstep  11961  mertenslem2  12063  nfcprod1  12081  nfcprod  12082  zproddc  12106  fprod2dlemstep  12149  ctiunctlemfo  13026  ellimc3apf  15350