Theorem dvelimdf 2077

Description: Deduction form of dvelimf 2076. (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 11-May-2018.)

Hypotheses

Ref	Expression
dvelimdf.1
dvelimdf.2
dvelimdf.3
dvelimdf.4
dvelimdf.5

Assertion

Ref	Expression
dvelimdf

Proof of Theorem dvelimdf

Step	Hyp	Ref	Expression
1		dvelimdf.1	. . . 4
2		dvelimdf.3	. . . 4
3	1, 2	nfim1 1919	. . 3
4		dvelimdf.2	. . . 4
5		dvelimdf.4	. . . 4
6	4, 5	nfim1 1919	. . 3
7		dvelimdf.5	. . . . 5
8	7	com12 31	. . . 4
9	8	pm5.74d 247	. . 3
10	3, 6, 9	dvelimf 2076	. 2
11		pm5.5 336	. . 3
12	1, 11	nfbidf 1887	. 2
13	10, 12	syl5ib 219	1

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

This theorem is referenced by:  nfsb4t  2130  dvelimdc  2642

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