Theorem abidnf 3268

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:   ,   ,

Proof of Theorem abidnf

Step	Hyp	Ref	Expression
1		sp 1859	. . 3
2		nfcr 2610	. . . 4
3	2	nfrd 1875	. . 3
4	1, 3	impbid2 204	. 2
5	4	abbi1dv 2595	1

Syntax hints:  ->wi 4  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442  F/_wnfc 2605

This theorem is referenced by:  dedhb  3269  nfopd  4234  nfimad  5351  nffvd  5880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607