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Theorem ax12inda2ALT 2276
 Description: Alternate proof of ax12inda2 2277, slightly more direct and not requiring ax-c16 2223. (Contributed by NM, 4-May-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax12inda2.1
Assertion
Ref Expression
ax12inda2ALT
Distinct variable group:   ,

Proof of Theorem ax12inda2ALT
StepHypRef Expression
1 ax-1 6 . . . . . . . 8
21axc4i-o 2229 . . . . . . 7
32a1i 11 . . . . . 6
4 biidd 237 . . . . . . 7
54dral1-o 2233 . . . . . 6
65imbi2d 316 . . . . . . 7
76dral2-o 2260 . . . . . 6
83, 5, 73imtr4d 268 . . . . 5
98aecoms-o 2231 . . . 4
109a1d 25 . . 3
1110a1d 25 . 2
12 simplr 755 . . . . 5
13 dveeq1-o 2265 . . . . . . . 8
1413naecoms-o 2257 . . . . . . 7
1514imp 429 . . . . . 6
1615adantlr 714 . . . . 5
17 hbnae-o 2258 . . . . . . 7
18 hba1-o 2228 . . . . . . 7
1917, 18hban 1931 . . . . . 6
20 ax-c5 2214 . . . . . . 7
21 ax12inda2.1 . . . . . . . 8
2221imp 429 . . . . . . 7
2320, 22sylan2 474 . . . . . 6
2419, 23alimdh 1638 . . . . 5
2512, 16, 24syl2anc 661 . . . 4
26 ax-11 1842 . . . . . 6
27 hbnae-o 2258 . . . . . . 7
28 hbnae-o 2258 . . . . . . . . 9
2928, 14nfdh 1879 . . . . . . . 8
30 19.21t 1904 . . . . . . . 8
3129, 30syl 16 . . . . . . 7
3227, 31albidh 1675 . . . . . 6
3326, 32syl5ib 219 . . . . 5
3433ad2antrr 725 . . . 4
3525, 34syld 44 . . 3
3635exp31 604 . 2
3711, 36pm2.61i 164 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 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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