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Theorem wl-ax11-lem3 31917
 Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.)
Assertion
Ref Expression
wl-ax11-lem3
Distinct variable group:   ,

Proof of Theorem wl-ax11-lem3
StepHypRef Expression
1 nfna1 1985 . 2
2 wl-naev 31862 . . . . 5
3 nfa1 1979 . . . . . . 7
4 nfna1 1985 . . . . . . 7
53, 4nfan 2011 . . . . . 6
6 axc11n 2143 . . . . . . . . . . 11
7 wl-aetr 31863 . . . . . . . . . . 11
86, 7syl5 33 . . . . . . . . . 10
98aecoms 2146 . . . . . . . . 9
109con3d 139 . . . . . . . 8
1110imdistani 696 . . . . . . 7
12 wl-ax11-lem2 31916 . . . . . . 7
1311, 12syl 17 . . . . . 6
145, 13alrimi 1955 . . . . 5
152, 14sylan2 477 . . . 4
1615expcom 437 . . 3
17 ax-wl-11v 31914 . . 3
1816, 17syl6 34 . 2
191, 18nfd 1956 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 371  wal 1442  wnf 1667 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933  ax-13 2091  ax-wl-11v 31914 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668 This theorem is referenced by:  wl-ax11-lem4  31918  wl-ax11-lem6  31920
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