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  5801  elabrex  5881  elabrexg  5882  nfmpo  6073  cbvmpox  6082  ovmpodxf  6130  fmpox  6346  f1od2  6381  nfrecs  6453  erovlem  6774  xpf1o  7005  mapxpen  7009  mkvprop  7325  cc3  7454  lble  9094  nfsum1  11867  nfsum  11868  zsumdc  11895  fsum3  11898  fsum3cvg2  11905  fsum2dlemstep  11945  mertenslem2  12047  nfcprod1  12065  nfcprod  12066  zproddc  12090  fprod2dlemstep  12133  ctiunctlemfo  13010  ellimc3apf  15334