Theorem dvelimhw 1955

Description: Proof of dvelimh 2078 without using ax-13 1999 but with additional distinct variable conditions. (Contributed by Andrew Salmon, 21-Jul-2011.) (Revised by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 23-Dec-2018.)

Hypotheses

Ref	Expression
dvelimhw.1
dvelimhw.2
dvelimhw.3
dvelimhw.4

Assertion

Ref	Expression
dvelimhw

Distinct variable groups:   ,   ,

Proof of Theorem dvelimhw

Step	Hyp	Ref	Expression
1		nfv 1707	. . . 4
2		equcom 1794	. . . . . 6
3		nfna1 1903	. . . . . . 7
4		dvelimhw.4	. . . . . . 7
5	3, 4	nfd 1878	. . . . . 6
6	2, 5	nfxfrd 1646	. . . . 5
7		dvelimhw.1	. . . . . . 7
8	7	nfi 1623	. . . . . 6
9	8	a1i 11	. . . . 5
10	6, 9	nfimd 1917	. . . 4
11	1, 10	nfald 1951	. . 3
12		dvelimhw.2	. . . . 5
13		dvelimhw.3	. . . . 5
14	12, 13	equsalhw 1945	. . . 4
15	14	nfbii 1644	. . 3
16	11, 15	sylib 196	. 2
17	16	nfrd 1875	1

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

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

This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617