Theorem nfeq2 2234

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

Hypothesis

Ref	Expression
nfeq2.1	|- F/_ x B

Assertion

Ref	Expression
nfeq2	|- F/ x A = B

Distinct variable group:   x, A

Allowed substitution hint:   B( x)

Proof of Theorem nfeq2

Step	Hyp	Ref	Expression
1		nfcv 2223	. 2 |- F/_ x A
2		nfeq2.1	. 2 |- F/_ x B
3	1, 2	nfeq 2230	1 |- F/ x A = B

Syntax hints:   = wceq 1285   F/wnf 1390   F/_wnfc 2210

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-cleq 2076  df-clel 2079  df-nfc 2212

This theorem is referenced by:  issetf  2617  eqvincf  2730  csbhypf  2952  nfpr  3466  intab  3691  nfmpt  3896  cbvmpt  3898  repizf2  3962  moop2  4042  eusvnf  4239  elrnmpt1  4644  fmptco  5406  elabrex  5477  nfmpt2  5652  cbvmpt2x  5661  ovmpt2dxf  5705  fmpt2x  5905  f1od2  5935  nfrecs  6004  erovlem  6314  xpf1o  6490  mapxpen  6494  lble  8302  nfsum1  10567  nfsum  10568