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Theorem ax12indalem 2275
 Description: Lemma for ax12inda2 2277 and ax12inda 2278. (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 2229 . . . . . . . 8
32a1i 11 . . . . . . 7
4 biidd 237 . . . . . . . 8
54dral1-o 2233 . . . . . . 7
65imbi2d 316 . . . . . . . 8
76dral2-o 2260 . . . . . . 7
83, 5, 73imtr4d 268 . . . . . 6
98aecoms-o 2231 . . . . 5
109a1d 25 . . . 4
1110a1d 25 . . 3
1211adantr 465 . 2
13 simplr 755 . . . . 5
14 aecom-o 2230 . . . . . . . . 9
1514con3i 135 . . . . . . . 8
16 aecom-o 2230 . . . . . . . . 9
1716con3i 135 . . . . . . . 8
18 axc9 2046 . . . . . . . . 9
1918imp 429 . . . . . . . 8
2015, 17, 19syl2an 477 . . . . . . 7
2120imp 429 . . . . . 6
2221adantlr 714 . . . . 5
23 hbnae-o 2258 . . . . . . 7
24 hba1-o 2228 . . . . . . 7
2523, 24hban 1931 . . . . . 6
26 ax-c5 2214 . . . . . . 7
27 ax12indalem.1 . . . . . . . 8
2827imp 429 . . . . . . 7
2926, 28sylan2 474 . . . . . 6
3025, 29alimdh 1638 . . . . 5
3113, 22, 30syl2anc 661 . . . 4
32 ax-11 1842 . . . . . 6
33 hbnae-o 2258 . . . . . . . 8
34 hbnae-o 2258 . . . . . . . 8
3533, 34hban 1931 . . . . . . 7
36 hbnae-o 2258 . . . . . . . . . 10
37 hbnae-o 2258 . . . . . . . . . 10
3836, 37hban 1931 . . . . . . . . 9
3938, 20nfdh 1879 . . . . . . . 8
40 19.21t 1904 . . . . . . . 8
4139, 40syl 16 . . . . . . 7
4235, 41albidh 1675 . . . . . 6
4332, 42syl5ib 219 . . . . 5
4443ad2antrr 725 . . . 4
4531, 44syld 44 . . 3
4645exp31 604 . 2
4712, 46pm2.61ian 790 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616 This theorem is referenced by:  ax12inda2  2277 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c9 2221 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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