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Theorem ax12-2 29079
 Description: Possible alternative to ax-12 1939. (Contributed by NM, 7-Nov-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax12-2

Proof of Theorem ax12-2
StepHypRef Expression
1 df-ex 1548 . 2
2 ax9 1942 . . . . 5
3 biidd 229 . . . . . 6
43dral1 1991 . . . . 5
52, 4mtbii 294 . . . 4
65pm2.21d 100 . . 3
7 19.8a 1754 . . . . . 6
8 exnal 1580 . . . . . 6
97, 8sylib 189 . . . . 5
109sps 1762 . . . 4
11 hbnae 1986 . . . . . . 7
12 hbnae 1986 . . . . . . 7
1311, 12hban 1840 . . . . . 6
14 hba1 1794 . . . . . 6
15 ax12o 1956 . . . . . . 7
1615imp 419 . . . . . 6
1713, 14, 16exlimdh 1816 . . . . 5
1817ex 424 . . . 4
1910, 18syl5 30 . . 3
206, 19pm2.61i 158 . 2
211, 20syl5bir 210 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1546  wex 1547 This theorem is referenced by:  ax12-3  29080  ax12OLD  29081 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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