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Theorem abidnf 2703
Description: Identity used to create closed-form versions of bound-variable hypothesis builders for class expressions. (Contributed by NM, 10-Nov-2005.) (Proof shortened by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
abidnf  F/_  {  |  }
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem abidnf
StepHypRef Expression
1 sp 1398 . . 3
2 nfcr 2167 . . . 4  F/_  F/
32nfrd 1410 . . 3  F/_
41, 3impbid2 131 . 2  F/_
54abbi1dv 2154 1  F/_  {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240   wceq 1242   wcel 1390   {cab 2023   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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  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-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164
This theorem is referenced by:  dedhb  2704  nfopd  3557  nfimad  4620  nffvd  5130
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