Theorem nfeq2 2396

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 2384	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfeq 2392	1 |- F/ x A = B

Syntax hints:   = wceq 1398   F/wnf 1509   F/_wnfc 2371

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-cleq 2225  df-clel 2228  df-nfc 2373

This theorem is referenced by:  issetf  2821  eqvincf  2942  csbhypf  3177  nfpr  3739  intab  3978  nfmpt  4202  cbvmptf  4204  cbvmpt  4205  repizf2  4275  moop2  4368  eusvnf  4574  elrnmpt1  5008  iotaexab  5331  fmptco  5843  elabrex  5930  elabrexg  5931  nfmpo  6122  cbvmpox  6131  ovmpodxf  6179  fmpox  6396  f1od2  6431  nfrecs  6538  erovlem  6861  xpf1o  7097  mapxpen  7101  mkvprop  7449  cc3  7582  lble  9221  nfsum1  12041  nfsum  12042  zsumdc  12070  fsum3  12073  fsum3cvg2  12080  fsum2dlemstep  12120  mertenslem2  12222  nfcprod1  12240  nfcprod  12241  zproddc  12265  fprod2dlemstep  12308  ctiunctlemfo  13190  ellimc3apf  15525