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Theorem bnj605 29255
 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 551 . . . 4
3 nfv 1609 . . . . . . 7
4319.41 1827 . . . . . 6
54exbii 1572 . . . . 5
6 bnj605.5 . . . . . . . 8
76bnj1095 29129 . . . . . . 7
87nfi 1541 . . . . . 6
9819.41 1827 . . . . 5
105, 9bitr2i 241 . . . 4
112, 10sylib 188 . . 3
12 bnj605.19 . . . . . . . . . 10
1312bnj1232 29152 . . . . . . . . 9
14 bnj219 29077 . . . . . . . . . 10
1512, 14bnj770 29109 . . . . . . . . 9
1613, 15jca 518 . . . . . . . 8
1716anim1i 551 . . . . . . 7
18 bnj170 29039 . . . . . . 7
1917, 18sylibr 203 . . . . . 6
20 bnj605.38 . . . . . 6
2119, 20syl 15 . . . . 5
22 simpl 443 . . . . 5
2321, 22jca 518 . . . 4
24232eximi 1567 . . 3
25 bnj248 29041 . . . . . . . 8
26 bnj605.31 . . . . . . . . . . 11
27 pm3.35 570 . . . . . . . . . . 11
2826, 27sylan2b 461 . . . . . . . . . 10
29 euex 2179 . . . . . . . . . 10
3028, 29syl 15 . . . . . . . . 9
31 bnj605.17 . . . . . . . . 9
3230, 31bnj1198 29144 . . . . . . . 8
3325, 32bnj832 29103 . . . . . . 7
34 bnj605.41 . . . . . . . . . . . . . 14
35 bnj605.42 . . . . . . . . . . . . . 14
36 bnj605.43 . . . . . . . . . . . . . 14
3734, 35, 363jca 1132 . . . . . . . . . . . . 13
38373com23 1157 . . . . . . . . . . . 12
39383expia 1153 . . . . . . . . . . 11
4039eximdv 1612 . . . . . . . . . 10
4140adantlr 695 . . . . . . . . 9
4241adantlr 695 . . . . . . . 8
4325, 42sylbi 187 . . . . . . 7
4433, 43mpd 14 . . . . . 6
45 bnj432 29057 . . . . . 6
46 biid 227 . . . . . . . 8
47 bnj605.13 . . . . . . . . 9
48 sbsbc 3008 . . . . . . . . . . 11
4948bicomi 193 . . . . . . . . . 10
50 sbid 1875 . . . . . . . . . 10
5149, 50bitri 240 . . . . . . . . 9
5247, 51bitri 240 . . . . . . . 8
53 bnj605.14 . . . . . . . . 9
54 sbsbc 3008 . . . . . . . . . . 11
5554bicomi 193 . . . . . . . . . 10
56 sbid 1875 . . . . . . . . . 10
5755, 56bitri 240 . . . . . . . . 9
5853, 57bitri 240 . . . . . . . 8
5946, 52, 583anbi123i 1140 . . . . . . 7
6059exbii 1572 . . . . . 6
6144, 45, 603imtr3i 256 . . . . 5
6261ex 423 . . . 4
6362exlimivv 1625 . . 3
6411, 24, 633syl 18 . 2
65643impa 1146 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wex 1531   wceq 1632  wsb 1638   wcel 1696  weu 2156   wne 2459  wral 2556  cvv 2801  wsbc 3004  c0 3468  ciun 3921   class class class wbr 4039   cep 4319   csuc 4410  com 4672   wfn 5266  cfv 5271  c1o 6488   w-bnj17 29027   c-bnj14 29029   w-bnj15 29033 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-eprel 4321  df-suc 4414  df-bnj17 29028
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