Theorem nfeq2 2241

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

Hypothesis

Ref	Expression
nfeq2.1	⊢ Ⅎ𝑥𝐵

Assertion

Ref	Expression
nfeq2	⊢ Ⅎ𝑥 𝐴 = 𝐵

Distinct variable group:   𝑥,𝐴

Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem nfeq2

Step	Hyp	Ref	Expression
1		nfcv 2229	. 2 ⊢ Ⅎ𝑥𝐴
2		nfeq2.1	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2237	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1290  Ⅎwnf 1395  Ⅎwnfc 2216

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-cleq 2082  df-clel 2085  df-nfc 2218

This theorem is referenced by:  issetf  2627  eqvincf  2743  csbhypf  2967  nfpr  3496  intab  3723  nfmpt  3936  cbvmptf  3938  cbvmpt  3939  repizf2  4003  moop2  4087  eusvnf  4288  elrnmpt1  4699  fmptco  5478  elabrex  5551  nfmpt2  5731  cbvmpt2x  5740  ovmpt2dxf  5784  fmpt2x  5984  f1od2  6014  nfrecs  6086  erovlem  6398  xpf1o  6614  mapxpen  6618  lble  8462  nfsum1  10799  nfsum  10800  zisum  10828  fisum  10832  fisumcvg2  10840  fsum3cvg2  10841  fsum2dlemstep  10882  mertenslem2  10984