Theorem nfeud2 2296

Description: Bound-variable hypothesis builder for uniqueness. (Contributed by Mario Carneiro, 14-Nov-2016.) (Proof shortened by Wolf Lammen, 4-Oct-2018.)

Hypotheses

Ref	Expression
nfeud2.1
nfeud2.2

Assertion

Ref	Expression
nfeud2

Proof of Theorem nfeud2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-eu 2286	. 2
2		nfv 1707	. . 3
3		nfeud2.1	. . . 4
4		nfeud2.2	. . . . 5
5		nfeqf1 2043	. . . . . 6
6	5	adantl 466	. . . . 5
7	4, 6	nfbid 1933	. . . 4
8	3, 7	nfald2 2073	. . 3
9	2, 8	nfexd 1952	. 2
10	1, 9	nfxfrd 1646	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  E!weu 2282

This theorem is referenced by:  nfmod2  2297  nfeud  2298  nfreud  3030

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286