Theorem nfeq2 2186

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 2175	. 2 ⊢ ℲxA
2		nfeq2.1	. 2 ⊢ ℲxB
3	1, 2	nfeq 2182	1 ⊢ Ⅎx A = B

Syntax hints:   = wceq 1242  Ⅎwnf 1346  Ⅎwnfc 2162

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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164

This theorem is referenced by:  issetf  2556  eqvincf  2663  csbhypf  2879  nfpr  3411  intab  3635  nfmpt  3840  cbvmpt  3842  repizf2  3906  moop2  3979  eusvnf  4151  elrnmpt1  4528  fmptco  5273  elabrex  5340  nfmpt2  5515  cbvmpt2x  5524  ovmpt2dxf  5568  fmpt2x  5768  nfrecs  5863  erovlem  6134