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Theorem bnj1030 29356
 Description: Technical lemma for bnj69 29379. 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
bnj1030.1
bnj1030.2
bnj1030.3
bnj1030.4
bnj1030.5
bnj1030.6
bnj1030.7
bnj1030.8
bnj1030.9
bnj1030.10
bnj1030.11
bnj1030.12
bnj1030.13
bnj1030.14
bnj1030.15
bnj1030.16
bnj1030.17
bnj1030.18
bnj1030.19
Assertion
Ref Expression
bnj1030
Distinct variable groups:   ,,,,,   ,,,,   ,,,,   ,   ,,   ,,,,,   ,   ,,,,   ,   ,   ,   ,,,,   ,,,,   ,   ,   ,
Allowed substitution hints:   (,,,,)   (,,,,,)   (,,,,)   ()   ()   (,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   ()   (,,,)   (,,,,,)   ()   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)

Proof of Theorem bnj1030
StepHypRef Expression
1 bnj1030.1 . 2
2 bnj1030.2 . 2
3 bnj1030.3 . 2
4 bnj1030.4 . 2
5 bnj1030.5 . 2
6 bnj1030.6 . 2
7 bnj1030.7 . 2
8 bnj1030.8 . 2
9 19.23vv 1915 . . . . 5
109albii 1575 . . . 4
11 19.23v 1914 . . . 4
1210, 11bitri 241 . . 3
13 bnj1030.9 . . . . 5
147bnj1071 29346 . . . . . . . 8
153, 14bnj769 29131 . . . . . . 7
1615bnj707 29123 . . . . . 6
17 bnj1030.10 . . . . . . 7
18 bnj1030.17 . . . . . . 7
19 bnj1030.18 . . . . . . 7
20 bnj1030.19 . . . . . . 7
212, 8, 13, 18bnj1123 29355 . . . . . . . . . 10
222, 3, 5, 7, 19, 20, 21bnj1118 29353 . . . . . . . . 9
231, 3, 5bnj1097 29350 . . . . . . . . 9
2422, 23bnj1109 29157 . . . . . . . 8
2524, 2, 3bnj1093 29349 . . . . . . 7
2613, 17, 18, 19, 20, 25bnj1090 29348 . . . . . 6
27 vex 2959 . . . . . . 7
2827, 17bnj110 29229 . . . . . 6
2916, 26, 28syl2anc 643 . . . . 5
304, 5, 3, 6, 13, 29, 8bnj1121 29354 . . . 4
3130gen2 1556 . . 3
3212, 31mpgbi 1558 . 2
331, 2, 3, 4, 5, 6, 7, 8, 32bnj1034 29339 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wal 1549  wex 1550   wceq 1652   wcel 1725  cab 2422  wral 2705  wrex 2706  cvv 2956  wsbc 3161   cdif 3317   wss 3320  c0 3628  csn 3814  ciun 4093   class class class wbr 4212   cep 4492   wfr 4538   csuc 4583  com 4845   cdm 4878   wfn 5449  cfv 5454   w-bnj17 29050   c-bnj14 29052   w-bnj15 29056   c-bnj18 29058   w-bnj19 29060 This theorem is referenced by:  bnj1124  29357 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-13 1727  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  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  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-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-tr 4303  df-eprel 4494  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-on 4585  df-lim 4586  df-suc 4587  df-om 4846  df-iota 5418  df-fn 5457  df-fv 5462  df-bnj17 29051  df-bnj18 29059  df-bnj19 29061
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