Theorem nfeq1 2921

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 2906	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2919	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1539  Ⅎwnf 1787  Ⅎwnfc 2886

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2118  ax-10 2139  ax-11 2156  ax-12 2173  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-nf 1788  df-cleq 2730  df-nfc 2888

This theorem is referenced by:  euabsn  4659  invdisjrabw  5055  invdisjrab  5056  disjxun  5068  iunopeqop  5429  fvelimad  6818  opabiotafun  6831  fvmptt  6877  eusvobj2  7248  oprabv  7313  ovmpodv2  7409  ov3  7413  dom2lem  8735  pwfseqlem2  10346  fsumf1o  15363  isummulc2  15402  fsum00  15438  isumshft  15479  zprod  15575  fprodf1o  15584  prodss  15585  fprodle  15634  iserodd  16464  yonedalem4b  17910  gsum2d2lem  19489  gsummptnn0fz  19502  gsummoncoe1  21385  elptr2  22633  ovoliunnul  24576  mbfinf  24734  itg2splitlem  24818  dgrle  25309  disjabrex  30822  disjabrexf  30823  disjunsn  30834  voliune  32097  volfiniune  32098  bnj958  32820  bnj1491  32937  ttrcltr  33702  noinfbnd1  33859  finminlem  34434  poimirlem23  35727  poimirlem28  35732  cdleme43fsv1snlem  38361  ltrniotaval  38522  cdlemksv2  38788  cdlemkuv2  38808  cdlemk36  38854  cdlemkid  38877  cdlemk19x  38884  eq0rabdioph  40514  monotoddzz  40681  disjinfi  42620  stoweidlem28  43459  stoweidlem48  43479  stoweidlem58  43489  etransclem32  43697  sge0gtfsumgt  43871  voliunsge0lem  43900