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Theorem bnj1033 29338
 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
bnj1033.1
bnj1033.2
bnj1033.3
bnj1033.4
bnj1033.5
bnj1033.6
bnj1033.7
bnj1033.8
bnj1033.9
bnj1033.10
Assertion
Ref Expression
bnj1033
Distinct variable groups:   ,,,,   ,,,,   ,   ,   ,,,,   ,   ,,,,   ,   ,,,,   ,,,,   ,
Allowed substitution hints:   (,,,)   (,,,,)   (,,,,)   ()   ()   (,,,,)   (,,,,)   (,,,)   (,,,)   (,,,,)

Proof of Theorem bnj1033
StepHypRef Expression
1 bnj1033.1 . . . . 5
2 bnj1033.2 . . . . 5
3 bnj1033.8 . . . . 5
4 bnj1033.9 . . . . 5
5 bnj1033.3 . . . . 5
61, 2, 3, 4, 5bnj983 29322 . . . 4
7 19.42v 1928 . . . . . . . . . 10
8 df-3an 938 . . . . . . . . . . 11
98exbii 1592 . . . . . . . . . 10
10 df-3an 938 . . . . . . . . . 10
117, 9, 103bitr4i 269 . . . . . . . . 9
1211exbii 1592 . . . . . . . 8
13 19.42v 1928 . . . . . . . . 9
1410exbii 1592 . . . . . . . . 9
15 df-3an 938 . . . . . . . . 9
1613, 14, 153bitr4i 269 . . . . . . . 8
1712, 16bitri 241 . . . . . . 7
1817exbii 1592 . . . . . 6
19 19.42v 1928 . . . . . . 7
2015exbii 1592 . . . . . . 7
21 df-3an 938 . . . . . . 7
2219, 20, 213bitr4i 269 . . . . . 6
2318, 22bitri 241 . . . . 5
24 bnj255 29069 . . . . . . . 8
25 bnj1033.7 . . . . . . . . . . 11
2625anbi2i 676 . . . . . . . . . 10
27 3anass 940 . . . . . . . . . 10
2826, 27bitr4i 244 . . . . . . . . 9
29283anbi3i 1146 . . . . . . . 8
3024, 29bitri 241 . . . . . . 7
31303exbii 1594 . . . . . 6
32 bnj1033.10 . . . . . 6
3331, 32sylbir 205 . . . . 5
3423, 33sylbir 205 . . . 4
356, 34syl3an3b 1222 . . 3
36353expia 1155 . 2
3736ssrdv 3354 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cab 2422  wral 2705  wrex 2706  cvv 2956   cdif 3317   wss 3320  c0 3628  csn 3814  ciun 4093   csuc 4583  com 4845   wfn 5449  cfv 5454   w-bnj17 29050   c-bnj14 29052   w-bnj15 29056   c-bnj18 29058   w-bnj19 29060 This theorem is referenced by:  bnj1034  29339 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-in 3327  df-ss 3334  df-iun 4095  df-fn 5457  df-bnj17 29051  df-bnj18 29059
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