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Theorem nfeq 2182
Description: Hypothesis builder for equality. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfnfc.1  F/_
nfeq.2  F/_
Assertion
Ref Expression
nfeq  F/

Proof of Theorem nfeq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2031 . 2
2 nfnfc.1 . . . . 5  F/_
32nfcri 2169 . . . 4  F/
4 nfeq.2 . . . . 5  F/_
54nfcri 2169 . . . 4  F/
63, 5nfbi 1478 . . 3  F/
76nfal 1465 . 2  F/
81, 7nfxfr 1360 1  F/
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1240   wceq 1242   F/wnf 1346   wcel 1390   F/_wnfc 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-bnd 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:  nfel  2183  nfeq1  2184  nfeq2  2186  nfne  2291  raleqf  2495  rexeqf  2496  reueq1f  2497  rmoeq1f  2498  rabeqf  2544  sbceqg  2860  csbhypf  2879  nfiotadxy  4813  nffn  4938  nffo  5048  fvmptdf  5201  mpteqb  5204  fvmptf  5206  eqfnfv2f  5212  dff13f  5352  ovmpt2s  5566  ov2gf  5567  ovmpt2dxf  5568  ovmpt2df  5574  eqerlem  6073
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