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Theorem nfeq2 2291
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
StepHypRef Expression
1 nfcv 2279 . 2  |-  F/_ x A
2 nfeq2.1 . 2  |-  F/_ x B
31, 2nfeq 2287 1  |-  F/ x  A  =  B
Colors of variables: wff set class
Syntax hints:    = wceq 1331   F/wnf 1436   F/_wnfc 2266
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2130  df-clel 2133  df-nfc 2268
This theorem is referenced by:  issetf  2688  eqvincf  2805  csbhypf  3033  nfpr  3568  intab  3795  nfmpt  4015  cbvmptf  4017  cbvmpt  4018  repizf2  4081  moop2  4168  eusvnf  4369  elrnmpt1  4785  fmptco  5579  elabrex  5652  nfmpo  5833  cbvmpox  5842  ovmpodxf  5889  fmpox  6091  f1od2  6125  nfrecs  6197  erovlem  6514  xpf1o  6731  mapxpen  6735  mkvprop  7025  lble  8698  nfsum1  11118  nfsum  11119  zsumdc  11146  fsum3  11149  fsum3cvg2  11156  fsum2dlemstep  11196  mertenslem2  11298  nfcprod1  11316  nfcprod  11317  ctiunctlemfo  11941  ellimc3apf  12787
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