Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  drnfc1 Unicode version

Theorem drnfc1 2194
 Description: Formula-building lemma for use with the Distinctor Reduction Theorem. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypothesis
Ref Expression
drnfc1.1
Assertion
Ref Expression
drnfc1

Proof of Theorem drnfc1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 drnfc1.1 . . . . 5
21eleq2d 2107 . . . 4
32drnf1 1621 . . 3
43dral2 1619 . 2
5 df-nfc 2167 . 2
6 df-nfc 2167 . 2
74, 5, 63bitr4g 212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  wnf 1349   wcel 1393  wnfc 2165 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-cleq 2033  df-clel 2036  df-nfc 2167 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator