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Theorem bnj1033 29850
 Description: Technical lemma for bnj69 29891. 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 29834 . . . 4
7 19.42v 1842 . . . . . . . . . 10
8 df-3an 1009 . . . . . . . . . . 11
98exbii 1726 . . . . . . . . . 10
10 df-3an 1009 . . . . . . . . . 10
117, 9, 103bitr4i 285 . . . . . . . . 9
1211exbii 1726 . . . . . . . 8
13 19.42v 1842 . . . . . . . . 9
1410exbii 1726 . . . . . . . . 9
15 df-3an 1009 . . . . . . . . 9
1613, 14, 153bitr4i 285 . . . . . . . 8
1712, 16bitri 257 . . . . . . 7
1817exbii 1726 . . . . . 6
19 19.42v 1842 . . . . . . 7
2015exbii 1726 . . . . . . 7
21 df-3an 1009 . . . . . . 7
2219, 20, 213bitr4i 285 . . . . . 6
2318, 22bitri 257 . . . . 5
24 bnj255 29582 . . . . . . . 8
25 bnj1033.7 . . . . . . . . . . 11
2625anbi2i 708 . . . . . . . . . 10
27 3anass 1011 . . . . . . . . . 10
2826, 27bitr4i 260 . . . . . . . . 9
29283anbi3i 1223 . . . . . . . 8
3024, 29bitri 257 . . . . . . 7
31303exbii 1728 . . . . . 6
32 bnj1033.10 . . . . . 6
3331, 32sylbir 218 . . . . 5
3423, 33sylbir 218 . . . 4
356, 34syl3an3b 1330 . . 3
36353expia 1233 . 2
3736ssrdv 3424 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   w3a 1007   wceq 1452  wex 1671   wcel 1904  cab 2457  wral 2756  wrex 2757  cvv 3031   cdif 3387   wss 3390  c0 3722  csn 3959  ciun 4269   csuc 5432   wfn 5584  cfv 5589  com 6711   w-bnj17 29563   c-bnj14 29565   w-bnj15 29569   c-bnj18 29571   w-bnj19 29573 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-v 3033  df-in 3397  df-ss 3404  df-iun 4271  df-fn 5592  df-bnj17 29564  df-bnj18 29572 This theorem is referenced by:  bnj1034  29851
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