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Theorem nfeq2 2331
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 2319 . 2  |-  F/_ x A
2 nfeq2.1 . 2  |-  F/_ x B
31, 2nfeq 2327 1  |-  F/ x  A  =  B
Colors of variables: wff set class
Syntax hints:    = wceq 1353   F/wnf 1460   F/_wnfc 2306
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-cleq 2170  df-clel 2173  df-nfc 2308
This theorem is referenced by:  issetf  2744  eqvincf  2862  csbhypf  3095  nfpr  3642  intab  3873  nfmpt  4095  cbvmptf  4097  cbvmpt  4098  repizf2  4162  moop2  4251  eusvnf  4453  elrnmpt1  4878  fmptco  5682  elabrex  5758  nfmpo  5943  cbvmpox  5952  ovmpodxf  5999  fmpox  6200  f1od2  6235  nfrecs  6307  erovlem  6626  xpf1o  6843  mapxpen  6847  mkvprop  7155  cc3  7266  lble  8903  nfsum1  11363  nfsum  11364  zsumdc  11391  fsum3  11394  fsum3cvg2  11401  fsum2dlemstep  11441  mertenslem2  11543  nfcprod1  11561  nfcprod  11562  zproddc  11586  fprod2dlemstep  11629  ctiunctlemfo  12439  ellimc3apf  14099
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