Theorem nfeq2 2387

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 2375	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfeq 2383	1 |- F/ x A = B

Syntax hints:   = wceq 1398   F/wnf 1509   F/_wnfc 2362

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 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-cleq 2224  df-clel 2227  df-nfc 2364

This theorem is referenced by:  issetf  2811  eqvincf  2932  csbhypf  3167  nfpr  3723  intab  3962  nfmpt  4186  cbvmptf  4188  cbvmpt  4189  repizf2  4258  moop2  4350  eusvnf  4556  elrnmpt1  4989  iotaexab  5312  fmptco  5821  elabrex  5908  elabrexg  5909  nfmpo  6100  cbvmpox  6109  ovmpodxf  6157  fmpox  6374  f1od2  6409  nfrecs  6516  erovlem  6839  xpf1o  7073  mapxpen  7077  mkvprop  7417  cc3  7547  lble  9186  nfsum1  11996  nfsum  11997  zsumdc  12025  fsum3  12028  fsum3cvg2  12035  fsum2dlemstep  12075  mertenslem2  12177  nfcprod1  12195  nfcprod  12196  zproddc  12220  fprod2dlemstep  12263  ctiunctlemfo  13140  ellimc3apf  15471