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Theorem ax12-2 27792
 Description: Possible alternative to ax-12 1633. (Contributed by NM, 7-Nov-1015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax12-2

Proof of Theorem ax12-2
StepHypRef Expression
1 df-ex 1538 . 2
2 ax-9 1684 . . . . 5
3 biidd 230 . . . . . 6
43dral1 1855 . . . . 5
52, 4mtbii 295 . . . 4
65pm2.21d 100 . . 3
7 19.8a 1758 . . . . . 6
8 exnal 1572 . . . . . 6
97, 8sylib 190 . . . . 5
109a4s 1700 . . . 4
11 hbnae 1844 . . . . . . 7
12 hbnae 1844 . . . . . . 7
1311, 12hban 1724 . . . . . 6
14 hba1 1718 . . . . . 6
15 ax-12o 1664 . . . . . . 7
1615imp 420 . . . . . 6
1713, 14, 16exlimdh 1785 . . . . 5
1817ex 425 . . . 4
1910, 18syl5 30 . . 3
206, 19pm2.61i 158 . 2
211, 20syl5bir 211 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wa 360  wal 1532  wex 1537 This theorem is referenced by:  ax12-3  27793  ax12OLD  27794 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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