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Theorem ax12olem2 2006
 Description: Lemma for nfeqf 2009 and dveeq1 2021. This lemma is equivalent to ax12v 1951 with one distinct variable constraint removed. (Contributed by Wolf Lammen, 29-Apr-2018.)
Assertion
Ref Expression
ax12olem2
Distinct variable group:   ,

Proof of Theorem ax12olem2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax12v 1951 . . . 4
2 ax-8 1687 . . . . . 6
32eximi 1585 . . . . 5
4 19.36v 1919 . . . . 5
53, 4sylib 189 . . . 4
61, 5syl9 68 . . 3
76alrimdv 1643 . 2
8 ax12olem1 2005 . 2
97, 8syl6ibr 219 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549  wex 1550 This theorem is referenced by:  ax12olem3  2007 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-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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