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Theorem dvelimhw 2079
 Description: Proof of dvelimh 2185 without using ax-13 2104 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:   ,   ,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem dvelimhw
StepHypRef Expression
1 nfv 1769 . . . 4
2 equcom 1870 . . . . . 6
3 nfna1 2005 . . . . . . 7
4 dvelimhw.4 . . . . . . 7
53, 4nfd 1976 . . . . . 6
62, 5nfxfrd 1705 . . . . 5
7 dvelimhw.1 . . . . . . 7
87nfi 1682 . . . . . 6
98a1i 11 . . . . 5
106, 9nfimd 2020 . . . 4
111, 10nfald 2053 . . 3
12 dvelimhw.2 . . . . 5
13 dvelimhw.3 . . . . 5
1412, 13equsalhw 2047 . . . 4
1514nfbii 1703 . . 3
1611, 15sylib 201 . 2
1716nfrd 1973 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189  wal 1450  wnf 1675 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676 This theorem is referenced by: (None)
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