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Theorem ax11indalem 2197
Description: Lemma for ax11inda2 2199 and ax11inda 2200. (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 5 . . . . . . . . 9
21a5i-o 2150 . . . . . . . 8
32a1i 10 . . . . . . 7
4 biidd 228 . . . . . . . 8
54dral1-o 2154 . . . . . . 7
65imbi2d 307 . . . . . . . 8
76dral2-o 2181 . . . . . . 7
83, 5, 73imtr4d 259 . . . . . 6
98aecoms-o 2152 . . . . 5
109a1d 22 . . . 4
1110a1d 22 . . 3
1211adantr 451 . 2
13 simplr 731 . . . . 5
14 aecom-o 2151 . . . . . . . . 9
1514con3i 127 . . . . . . . 8
16 aecom-o 2151 . . . . . . . . 9
1716con3i 127 . . . . . . . 8
18 ax12o 1934 . . . . . . . . 9
1918imp 418 . . . . . . . 8
2015, 17, 19syl2an 463 . . . . . . 7
2120imp 418 . . . . . 6
2221adantlr 695 . . . . 5
23 hbnae-o 2179 . . . . . . 7
24 hba1-o 2149 . . . . . . 7
2523, 24hban 1828 . . . . . 6
26 ax-4 2135 . . . . . . 7
27 ax11indalem.1 . . . . . . . 8
2827imp 418 . . . . . . 7
2926, 28sylan2 460 . . . . . 6
3025, 29alimdh 1563 . . . . 5
3113, 22, 30syl2anc 642 . . . 4
32 ax-7 1734 . . . . . 6
33 hbnae-o 2179 . . . . . . . 8
34 hbnae-o 2179 . . . . . . . 8
3533, 34hban 1828 . . . . . . 7
36 hbnae-o 2179 . . . . . . . . . 10
37 hbnae-o 2179 . . . . . . . . . 10
3836, 37hban 1828 . . . . . . . . 9
3938, 20nfdh 1767 . . . . . . . 8  F/
40 19.21t 1795 . . . . . . . 8  F/
4139, 40syl 15 . . . . . . 7
4235, 41albidh 1590 . . . . . 6
4332, 42syl5ib 210 . . . . 5
4443ad2antrr 706 . . . 4
4531, 44syld 40 . . 3
4645exp31 587 . 2
4712, 46pm2.61ian 765 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540   F/wnf 1544
This theorem is referenced by:  ax11inda2  2199
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-4 2135  ax-5o 2136  ax-6o 2137  ax-10o 2139  ax-12o 2142
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
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