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Theorem ax12olem3 2007
 Description: Lemma for nfeqf 2009 and dveeq1 2021. Convert ax12olem2 2006 into a more general form. (Contributed by Wolf Lammen, 29-Apr-2018.)
Hypothesis
Ref Expression
ax12olem3.1
Assertion
Ref Expression
ax12olem3
Distinct variable group:   ,

Proof of Theorem ax12olem3
StepHypRef Expression
1 exnal 1583 . 2
2 nfnf1 1808 . . 3
3 ax12olem2 2006 . . . . 5
4 ax12olem3.1 . . . . 5
53, 4syld 42 . . . 4
6 nf2 1889 . . . 4
75, 6sylibr 204 . . 3
82, 7exlimi 1821 . 2
91, 8sylbir 205 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549  wex 1550  wnf 1553 This theorem is referenced by:  nfeqf  2009  dveeq1  2021 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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