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Theorem abidnf 2947
 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 1728 . . 3
2 nfcr 2424 . . . 4
32nfrd 1755 . . 3
41, 3impbid2 195 . 2
54abbi1dv 2412 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1530   wceq 1632   wcel 1696  cab 2282  wnfc 2419 This theorem is referenced by:  dedhb  2948  nfopd  3829  nfimad  5037  nffvd  5550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421
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