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Theorem nfeq2 2205
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 2194 . 2 𝑥𝐴
2 nfeq2.1 . 2 𝑥𝐵
31, 2nfeq 2201 1 𝑥 𝐴 = 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1259  wnf 1365  wnfc 2181
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-cleq 2049  df-clel 2052  df-nfc 2183
This theorem is referenced by:  issetf  2579  eqvincf  2692  csbhypf  2913  nfpr  3448  intab  3672  nfmpt  3877  cbvmpt  3879  repizf2  3943  moop2  4016  eusvnf  4213  elrnmpt1  4613  fmptco  5358  elabrex  5425  nfmpt2  5601  cbvmpt2x  5610  ovmpt2dxf  5654  fmpt2x  5854  f1od2  5884  nfrecs  5953  erovlem  6229  nfsum1  10106  nfsum  10107
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