ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfeq Structured version   Unicode version

Theorem nfeq 2167
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 2016 . 2
2 nfnfc.1 . . . . 5  F/_
32nfcri 2154 . . . 4  F/
4 nfeq.2 . . . . 5  F/_
54nfcri 2154 . . . 4  F/
63, 5nfbi 1463 . . 3  F/
76nfal 1450 . 2  F/
81, 7nfxfr 1343 1  F/
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1226   wceq 1228   F/wnf 1329   wcel 1374   F/_wnfc 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:  nfel  2168  nfeq1  2169  nfeq2  2171  nfne  2275  raleqf  2479  rexeqf  2480  reueq1f  2481  rmoeq1f  2482  rabeqf  2528  sbceqg  2843  csbhypf  2862  nfiotadxy  4797  nffn  4921  nffo  5030  fvmptdf  5183  mpteqb  5186  fvmptf  5188  eqfnfv2f  5194  dff13f  5334  ovmpt2s  5547  ov2gf  5548  ovmpt2dxf  5549  ovmpt2df  5555  eqerlem  6048
  Copyright terms: Public domain W3C validator