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Theorem ax12indalem 32485
 Description: Lemma for ax12inda2 32487 and ax12inda 32488. (Contributed by NM, 24-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax12indalem.1
Assertion
Ref Expression
ax12indalem

Proof of Theorem ax12indalem
StepHypRef Expression
1 ax-1 6 . . . . . . . . 9
21axc4i-o 32439 . . . . . . . 8
32a1i 11 . . . . . . 7
4 biidd 240 . . . . . . . 8
54dral1-o 32443 . . . . . . 7
65imbi2d 317 . . . . . . . 8
76dral2-o 32470 . . . . . . 7
83, 5, 73imtr4d 271 . . . . . 6
98aecoms-o 32441 . . . . 5
109a1d 26 . . . 4
1110a1d 26 . . 3
13 simplr 760 . . . . 5
14 aecom-o 32440 . . . . . . . . 9
1514con3i 140 . . . . . . . 8
16 aecom-o 32440 . . . . . . . . 9
1716con3i 140 . . . . . . . 8
18 axc9 2105 . . . . . . . . 9
1918imp 430 . . . . . . . 8
2015, 17, 19syl2an 479 . . . . . . 7
2120imp 430 . . . . . 6
2221adantlr 719 . . . . 5
23 hbnae-o 32468 . . . . . . 7
24 hba1-o 32438 . . . . . . 7
2523, 24hban 1991 . . . . . 6
26 ax-c5 32424 . . . . . . 7
27 ax12indalem.1 . . . . . . . 8
2827imp 430 . . . . . . 7
2926, 28sylan2 476 . . . . . 6
3025, 29alimdh 1683 . . . . 5
3113, 22, 30syl2anc 665 . . . 4
32 ax-11 1896 . . . . . 6
33 hbnae-o 32468 . . . . . . . 8
34 hbnae-o 32468 . . . . . . . 8
3533, 34hban 1991 . . . . . . 7
36 hbnae-o 32468 . . . . . . . . . 10
37 hbnae-o 32468 . . . . . . . . . 10
3836, 37hban 1991 . . . . . . . . 9
3938, 20nfdh 1934 . . . . . . . 8
40 19.21t 1963 . . . . . . . 8
4139, 40syl 17 . . . . . . 7
4235, 41albidh 1720 . . . . . 6
4332, 42syl5ib 222 . . . . 5
4443ad2antrr 730 . . . 4
4531, 44syld 45 . . 3
4645exp31 607 . 2
4712, 46pm2.61ian 797 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wa 370  wal 1435  wnf 1661 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-c5 32424  ax-c4 32425  ax-c7 32426  ax-c11 32428  ax-c9 32431 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662 This theorem is referenced by:  ax12inda2  32487
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