Theorem nfeq1 2915

Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
nfeq1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfeq1	⊢ Ⅎ𝑥 𝐴 = 𝐵

Distinct variable group:   𝑥,𝐵

Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfeq1

Step	Hyp	Ref	Expression
1		nfeq1.1	. 2 ⊢ Ⅎ𝑥𝐴
2		nfcv 2899	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2913	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1542  Ⅎwnf 1785  Ⅎwnfc 2884

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-nf 1786  df-cleq 2729  df-nfc 2886

This theorem is referenced by:  euabsn  4671  invdisjrab  5073  disjxun  5084  iunopeqop  5467  fvelimad  6899  opabiotafun  6912  fvmptt  6960  eusvobj2  7350  oprabv  7418  ovmpodv2  7516  ov3  7521  dom2lem  8930  ttrcltr  9626  pwfseqlem2  10571  fsumf1o  15674  isummulc2  15713  fsum00  15750  isumshft  15793  zprod  15891  fprodf1o  15900  prodss  15901  fprodle  15950  iserodd  16795  yonedalem4b  18231  gsum2d2lem  19937  gsummptnn0fz  19950  gsummoncoe1  22282  elptr2  23548  ovoliunnul  25483  mbfinf  25641  itg2splitlem  25724  dgrle  26220  noinfbnd1  27712  disjabrex  32672  disjabrexf  32673  disjunsn  32684  voliune  34394  volfiniune  34395  bnj958  35103  bnj1491  35220  finminlem  36521  poimirlem23  37975  poimirlem28  37980  cdleme43fsv1snlem  40877  ltrniotaval  41038  cdlemksv2  41304  cdlemkuv2  41324  cdlemk36  41370  cdlemkid  41393  cdlemk19x  41400  eq0rabdioph  43219  monotoddzz  43386  disjinfi  45637  dvnprodlem1  46389  stoweidlem28  46471  stoweidlem48  46491  stoweidlem58  46501  etransclem32  46709  sge0f1o  46825  sge0gtfsumgt  46886  voliunsge0lem  46915