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Theorem ax11inda2ALT 2198
 Description: A proof of ax11inda2 2199 that is slightly more direct. (Contributed by NM, 4-May-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax11inda2.1
Assertion
Ref Expression
ax11inda2ALT
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem ax11inda2ALT
StepHypRef Expression
1 ax-1 6 . . . . . . . 8
21a5i-o 2150 . . . . . . 7
32a1i 10 . . . . . 6
4 biidd 228 . . . . . . 7
54dral1-o 2154 . . . . . 6
65imbi2d 307 . . . . . . 7
76dral2-o 2181 . . . . . 6
83, 5, 73imtr4d 259 . . . . 5
98aecoms-o 2152 . . . 4
109a1d 22 . . 3
1110a1d 22 . 2
12 simplr 731 . . . . 5
13 dveeq1-o 2187 . . . . . . . 8
1413naecoms-o 2178 . . . . . . 7
1514imp 418 . . . . . 6
1615adantlr 695 . . . . 5
17 hbnae-o 2179 . . . . . . 7
18 hba1-o 2149 . . . . . . 7
1917, 18hban 1828 . . . . . 6
20 ax-4 2135 . . . . . . 7
21 ax11inda2.1 . . . . . . . 8
2221imp 418 . . . . . . 7
2320, 22sylan2 460 . . . . . 6
2419, 23alimdh 1563 . . . . 5
2512, 16, 24syl2anc 642 . . . 4
26 ax-7 1734 . . . . . 6
27 hbnae-o 2179 . . . . . . 7
28 hbnae-o 2179 . . . . . . . . 9
2928, 14nfdh 1767 . . . . . . . 8
30 19.21t 1795 . . . . . . . 8
3129, 30syl 15 . . . . . . 7
3227, 31albidh 1590 . . . . . 6
3326, 32syl5ib 210 . . . . 5
3433ad2antrr 706 . . . 4
3525, 34syld 40 . . 3
3635exp31 587 . 2
3711, 36pm2.61i 156 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540  wnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem is referenced by: (None)
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