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Theorem nfceqdf 2298
 Description: An equality theorem for effectively not free. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfceqdf.1
nfceqdf.2
Assertion
Ref Expression
nfceqdf

Proof of Theorem nfceqdf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfceqdf.1 . . . 4
2 nfceqdf.2 . . . . 5
32eleq2d 2227 . . . 4
41, 3nfbidf 1519 . . 3
54albidv 1804 . 2
6 df-nfc 2288 . 2
7 df-nfc 2288 . 2
85, 6, 73bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1333   wceq 1335  wnf 1440   wcel 2128  wnfc 2286 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-17 1506  ax-ial 1514  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-cleq 2150  df-clel 2153  df-nfc 2288 This theorem is referenced by:  nfopd  3758  dfnfc2  3790  nfimad  4936  nffvd  5479
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