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Theorem ax12olem2 1881
 Description: Lemma for ax12o 1887. Negate the equalities in ax-12 1878, shown as the hypothesis. (Contributed by NM, 24-Dec-2015.)
Hypothesis
Ref Expression
ax12olem2.1
Assertion
Ref Expression
ax12olem2
Distinct variable groups:   ,,   ,

Proof of Theorem ax12olem2
StepHypRef Expression
1 ax12olem2.1 . . . . . 6
21anim1d 547 . . . . 5
3 ax-17 1606 . . . . . . 7
43anim2i 552 . . . . . 6
5 19.26 1583 . . . . . 6
64, 5sylibr 203 . . . . 5
72, 6syl6 29 . . . 4
87eximdv 1612 . . 3
9 19.12 1746 . . 3
108, 9syl6 29 . 2
11 ax12olem1 1880 . 2
1211albii 1556 . 2
1310, 11, 123imtr3g 260 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1530  wex 1531 This theorem is referenced by:  ax12olem4  1883 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-7 1720  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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