Theorem nfreud 3030

Description: Deduction version of nfreu 3032. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 8-Oct-2016.)

Hypotheses

Ref	Expression
nfreud.1
nfreud.2
nfreud.3

Assertion

Ref	Expression
nfreud

Proof of Theorem nfreud

Step	Hyp	Ref	Expression
1		df-reu 2814	. 2
2		nfreud.1	. . 3
3		nfcvf 2644	. . . . . 6
4	3	adantl 466	. . . . 5
5		nfreud.2	. . . . . 6
6	5	adantr 465	. . . . 5
7	4, 6	nfeld 2627	. . . 4
8		nfreud.3	. . . . 5
9	8	adantr 465	. . . 4
10	7, 9	nfand 1925	. . 3
11	2, 10	nfeud2 2296	. 2
12	1, 11	nfxfrd 1646	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  F/wnf 1616  e.wcel 1818  E!weu 2282  F/_wnfc 2605  E!wreu 2809

This theorem is referenced by:  nfreu  3032

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-eu 2286  df-cleq 2449  df-clel 2452  df-nfc 2607  df-reu 2814