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Theorem abidnf 3103
 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
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem abidnf
StepHypRef Expression
1 sp 1763 . . 3
2 nfcr 2564 . . . 4
32nfrd 1779 . . 3
41, 3impbid2 196 . 2
54abbi1dv 2552 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549   wceq 1652   wcel 1725  cab 2422  wnfc 2559 This theorem is referenced by:  dedhb  3104  nfopd  4001  nfimad  5212  nffvd  5737 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561
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