Theorem nfeq2 2171

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 2160	. 2 ⊢ ℲxA
2		nfeq2.1	. 2 ⊢ ℲxB
3	1, 2	nfeq 2167	1 ⊢ Ⅎx A = B

Syntax hints:   = wceq 1228  Ⅎwnf 1329  Ⅎwnfc 2147

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004

This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-cleq 2015  df-clel 2018  df-nfc 2149

This theorem is referenced by:  issetf  2540  eqvincf  2646  csbhypf  2862  nfpr  3394  intab  3618  nfmpt  3823  cbvmpt  3825  repizf2  3889  moop2  3962  eusvnf  4135  elrnmpt1  4512  fmptco  5255  elabrex  5322  nfmpt2  5496  cbvmpt2x  5505  ovmpt2dxf  5549  fmpt2x  5749  nfrecs  5844  erovlem  6109