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Theorem ax12olem5 1884
 Description: Lemma for ax12o 1887. See ax12olem6 1885 for derivation of ax12o 1887 from the conclusion. (Contributed by NM, 24-Dec-2015.)
Hypothesis
Ref Expression
ax12olem5.1
Assertion
Ref Expression
ax12olem5

Proof of Theorem ax12olem5
StepHypRef Expression
1 exnal 1564 . 2
2 19.8a 1730 . . 3
3 hbe1 1717 . . . . 5
4 hba1 1731 . . . . 5
53, 4hbim 1737 . . . 4
6 df-ex 1532 . . . . 5
7 ax12olem5.1 . . . . 5
86, 7syl5bi 208 . . . 4
95, 8exlimih 1741 . . 3
102, 9syl5 28 . 2
111, 10sylbir 204 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1530  wex 1531 This theorem is referenced by:  ax12olem7  1886  ax12olem7NEW7  29437 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-ex 1532
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