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Theorem bnj605 29278
 Description: Technical lemma. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj605.5
bnj605.13
bnj605.14
bnj605.17
bnj605.19
bnj605.28
bnj605.31
bnj605.32
bnj605.33
bnj605.37
bnj605.38
bnj605.41
bnj605.42
bnj605.43
Assertion
Ref Expression
bnj605
Distinct variable groups:   ,,   ,,   ,,   ,   ,   ,   ,   ,   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,,,)   (,,,,,)   (,,,,,,)   (,,,,,)   (,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)

Proof of Theorem bnj605
StepHypRef Expression
1 bnj605.37 . . . . 5
21anim1i 552 . . . 4
3 nfv 1629 . . . . . . 7
4319.41 1900 . . . . . 6
54exbii 1592 . . . . 5
6 bnj605.5 . . . . . . . 8
76bnj1095 29152 . . . . . . 7
87nfi 1560 . . . . . 6
9819.41 1900 . . . . 5
105, 9bitr2i 242 . . . 4
112, 10sylib 189 . . 3
12 bnj605.19 . . . . . . . . . 10
1312bnj1232 29175 . . . . . . . . 9
14 bnj219 29100 . . . . . . . . . 10
1512, 14bnj770 29132 . . . . . . . . 9
1613, 15jca 519 . . . . . . . 8
1716anim1i 552 . . . . . . 7
18 bnj170 29062 . . . . . . 7
1917, 18sylibr 204 . . . . . 6
20 bnj605.38 . . . . . 6
2119, 20syl 16 . . . . 5
22 simpl 444 . . . . 5
2321, 22jca 519 . . . 4
24232eximi 1586 . . 3
25 bnj248 29064 . . . . . . . 8
26 bnj605.31 . . . . . . . . . . 11
27 pm3.35 571 . . . . . . . . . . 11
2826, 27sylan2b 462 . . . . . . . . . 10
29 euex 2304 . . . . . . . . . 10
3028, 29syl 16 . . . . . . . . 9
31 bnj605.17 . . . . . . . . 9
3230, 31bnj1198 29167 . . . . . . . 8
3325, 32bnj832 29126 . . . . . . 7
34 bnj605.41 . . . . . . . . . . . . . 14
35 bnj605.42 . . . . . . . . . . . . . 14
36 bnj605.43 . . . . . . . . . . . . . 14
3734, 35, 363jca 1134 . . . . . . . . . . . . 13
38373com23 1159 . . . . . . . . . . . 12
39383expia 1155 . . . . . . . . . . 11
4039eximdv 1632 . . . . . . . . . 10
4140adantlr 696 . . . . . . . . 9
4241adantlr 696 . . . . . . . 8
4325, 42sylbi 188 . . . . . . 7
4433, 43mpd 15 . . . . . 6
45 bnj432 29080 . . . . . 6
46 biid 228 . . . . . . . 8
47 bnj605.13 . . . . . . . . 9
48 sbcid 3177 . . . . . . . . 9
4947, 48bitri 241 . . . . . . . 8
50 bnj605.14 . . . . . . . . 9
51 sbcid 3177 . . . . . . . . 9
5250, 51bitri 241 . . . . . . . 8
5346, 49, 523anbi123i 1142 . . . . . . 7
5453exbii 1592 . . . . . 6
5544, 45, 543imtr3i 257 . . . . 5
5655ex 424 . . . 4
5756exlimivv 1645 . . 3
5811, 24, 573syl 19 . 2
59583impa 1148 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  weu 2281   wne 2599  wral 2705  cvv 2956  wsbc 3161  c0 3628  ciun 4093   class class class wbr 4212   cep 4492   csuc 4583  com 4845   wfn 5449  cfv 5454  c1o 6717   w-bnj17 29050   c-bnj14 29052   w-bnj15 29056 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-eprel 4494  df-suc 4587  df-bnj17 29051
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