Theorem dvelimf 2076

Description: Version of dvelimv 2080 without any variable restrictions. (Contributed by NM, 1-Oct-2002.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 11-May-2018.)

Hypotheses

Ref	Expression
dvelimf.1
dvelimf.2
dvelimf.3

Assertion

Ref	Expression
dvelimf

Proof of Theorem dvelimf

Step	Hyp	Ref	Expression
1		dvelimf.2	. . . 4
2		dvelimf.3	. . . 4
3	1, 2	equsal 2036	. . 3
4	3	bicomi 202	. 2
5		nfnae 2058	. . 3
6		nfeqf 2045	. . . . 5
7	6	ancoms 453	. . . 4
8		dvelimf.1	. . . . 5
9	8	a1i 11	. . . 4
10	7, 9	nfimd 1917	. . 3
11	5, 10	nfald2 2073	. 2
12	4, 11	nfxfrd 1646	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616

This theorem is referenced by:  dvelimdf  2077  dvelimh  2078  dvelimnf  2081

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