Theorem nfbrd 4495

Description: Deduction version of bound-variable hypothesis builder nfbr 4496. (Contributed by NM, 13-Dec-2005.) (Revised by Mario Carneiro, 14-Oct-2016.)

Hypotheses

Ref	Expression
nfbrd.2
nfbrd.3
nfbrd.4

Assertion

Ref	Expression
nfbrd

Proof of Theorem nfbrd

Step	Hyp	Ref	Expression
1		df-br 4453	. 2
2		nfbrd.2	. . . 4
3		nfbrd.4	. . . 4
4	2, 3	nfopd 4234	. . 3
5		nfbrd.3	. . 3
6	4, 5	nfeld 2627	. 2
7	1, 6	nfxfrd 1646	1

Syntax hints:  ->wi 4  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  <.cop 4035   class class class wbr 4452

This theorem is referenced by:  nfbr  4496

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-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453