MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dvelimhw Unicode version

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
StepHypRef Expression
1 nfv 1707 . . . 4
2 equcom 1794 . . . . . 6
3 nfna1 1903 . . . . . . 7
4 dvelimhw.4 . . . . . . 7
53, 4nfd 1878 . . . . . 6
62, 5nfxfrd 1646 . . . . 5
7 dvelimhw.1 . . . . . . 7
87nfi 1623 . . . . . 6
98a1i 11 . . . . 5
106, 9nfimd 1917 . . . 4
111, 10nfald 1951 . . 3
12 dvelimhw.2 . . . . 5
13 dvelimhw.3 . . . . 5
1412, 13equsalhw 1945 . . . 4
1514nfbii 1644 . . 3
1611, 15sylib 196 . 2
1716nfrd 1875 1
Colors of variables: wff setvar class
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
  Copyright terms: Public domain W3C validator