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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 𝑥𝐵
Assertion
Ref Expression
nfeq2 𝑥 𝐴 = 𝐵
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem nfeq2
StepHypRef Expression
1 nfcv 2319 . 2 𝑥𝐴
2 nfeq2.1 . 2 𝑥𝐵
31, 2nfeq 2327 1 𝑥 𝐴 = 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1353  wnf 1460  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  2746  eqvincf  2864  csbhypf  3097  nfpr  3644  intab  3875  nfmpt  4097  cbvmptf  4099  cbvmpt  4100  repizf2  4164  moop2  4253  eusvnf  4455  elrnmpt1  4880  fmptco  5685  elabrex  5761  elabrexg  5762  nfmpo  5947  cbvmpox  5956  ovmpodxf  6003  fmpox  6204  f1od2  6239  nfrecs  6311  erovlem  6630  xpf1o  6847  mapxpen  6851  mkvprop  7159  cc3  7270  lble  8907  nfsum1  11367  nfsum  11368  zsumdc  11395  fsum3  11398  fsum3cvg2  11405  fsum2dlemstep  11445  mertenslem2  11547  nfcprod1  11565  nfcprod  11566  zproddc  11590  fprod2dlemstep  11633  ctiunctlemfo  12443  ellimc3apf  14317
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