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Theorem ax12olem3 1882
 Description: Lemma for ax12o 1887. Show the equivalence of an intermediate equivalent to ax12o 1887 with the conjunction of ax-12 1878 and a variant with negated equalities. (Contributed by NM, 24-Dec-2015.)
Assertion
Ref Expression
ax12olem3

Proof of Theorem ax12olem3
StepHypRef Expression
1 sp 1728 . . . . . 6
21con2i 112 . . . . 5
32imim1i 54 . . . 4
43imim2i 13 . . 3
5 sp 1728 . . . . . 6
65imim2i 13 . . . . 5
76con1d 116 . . . 4
87imim2i 13 . . 3
94, 8jca 518 . 2
10 con1 120 . . . . . 6
1110imim1d 69 . . . . 5
1211com12 27 . . . 4
1312imim3i 55 . . 3
1413imp 418 . 2
159, 14impbii 180 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1530 This theorem is referenced by:  ax12olem4  1883  ax12olem4wAUX7  29435  ax12olem4OLD7  29661 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-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360
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