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Theorem dvelimhw 1876
 Description: Proof of dvelimh 2067 without using ax-12 1950 but with additional distinct variable conditions. (Contributed by Andrew Salmon, 21-Jul-2011.) (Revised by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 3-Mar-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 1629 . . . 4
2 equcom 1692 . . . . . 6
3 nfa1 1806 . . . . . . . 8
43nfn 1811 . . . . . . 7
5 dvelimhw.4 . . . . . . 7
64, 5nfd 1782 . . . . . 6
72, 6nfxfrd 1580 . . . . 5
8 dvelimhw.1 . . . . . . 7
98nfi 1560 . . . . . 6
109a1i 11 . . . . 5
117, 10nfimd 1827 . . . 4
121, 11nfald 1871 . . 3
13 dvelimhw.2 . . . . 5
14 dvelimhw.3 . . . . 5
1513, 14equsalhw 1860 . . . 4
1615nfbii 1578 . . 3
1712, 16sylib 189 . 2
1817nfrd 1779 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1549  wnf 1553 This theorem is referenced by:  ax12olem6OLD  2016 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-tru 1328  df-ex 1551  df-nf 1554
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