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Theorem ax11indalem 2276
 Description: Lemma for ax11inda2 2278 and ax11inda 2279. (Contributed by NM, 24-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax11indalem.1
Assertion
Ref Expression
ax11indalem

Proof of Theorem ax11indalem
StepHypRef Expression
1 ax-1 6 . . . . . . . . 9
21a5i-o 2229 . . . . . . . 8
32a1i 11 . . . . . . 7
4 biidd 230 . . . . . . . 8
54dral1-o 2233 . . . . . . 7
65imbi2d 309 . . . . . . . 8
76dral2-o 2260 . . . . . . 7
83, 5, 73imtr4d 261 . . . . . 6
98aecoms-o 2231 . . . . 5
109a1d 24 . . . 4
1110a1d 24 . . 3
13 simplr 733 . . . . 5
14 aecom-o 2230 . . . . . . . . 9
1514con3i 130 . . . . . . . 8
16 aecom-o 2230 . . . . . . . . 9
1716con3i 130 . . . . . . . 8
18 ax12o 2011 . . . . . . . . 9
1918imp 420 . . . . . . . 8
2015, 17, 19syl2an 465 . . . . . . 7
2120imp 420 . . . . . 6
2221adantlr 697 . . . . 5
23 hbnae-o 2258 . . . . . . 7
24 hba1-o 2228 . . . . . . 7
2523, 24hban 1851 . . . . . 6
26 ax-4 2214 . . . . . . 7
27 ax11indalem.1 . . . . . . . 8
2827imp 420 . . . . . . 7
2926, 28sylan2 462 . . . . . 6
3025, 29alimdh 1573 . . . . 5
3113, 22, 30syl2anc 644 . . . 4
32 ax-7 1750 . . . . . 6
33 hbnae-o 2258 . . . . . . . 8
34 hbnae-o 2258 . . . . . . . 8
3533, 34hban 1851 . . . . . . 7
36 hbnae-o 2258 . . . . . . . . . 10
37 hbnae-o 2258 . . . . . . . . . 10
3836, 37hban 1851 . . . . . . . . 9
3938, 20nfdh 1784 . . . . . . . 8
40 19.21t 1814 . . . . . . . 8
4139, 40syl 16 . . . . . . 7
4235, 41albidh 1601 . . . . . 6
4332, 42syl5ib 212 . . . . 5
4443ad2antrr 708 . . . 4
4531, 44syld 43 . . 3
4645exp31 589 . 2
4712, 46pm2.61ian 767 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550  wnf 1554 This theorem is referenced by:  ax11inda2  2278 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-4 2214  ax-5o 2215  ax-6o 2216  ax-10o 2218  ax-12o 2221 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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