Theorem nfeq1 2318

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 2308	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2316	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1343  Ⅎwnf 1448  Ⅎwnfc 2295

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-cleq 2158  df-clel 2161  df-nfc 2297

This theorem is referenced by:  euabsn  3646  fvmptt  5577  eusvobj2  5828  ovmpodv2  5975  ovi3  5978  dom2lem  6738  seq3f1olemstep  10436  seq3f1olemp  10437  fsumf1o  11331  isumss  11332  isummulc2  11367  fsum00  11403  isumshft  11431  fprodf1o  11529  prodssdc  11530