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Theorem bnj571 29214
 Description: Technical lemma for bnj852 29229. 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
bnj571.3
bnj571.16
bnj571.17
bnj571.18
bnj571.19
bnj571.20
bnj571.22
bnj571.23
bnj571.24
bnj571.25
bnj571.26
bnj571.29
bnj571.30
bnj571.38
bnj571.21
bnj571.40
bnj571.33
Assertion
Ref Expression
bnj571
Distinct variable groups:   ,,,   ,   ,,,   ,   ,,,   ,,   ,,
Allowed substitution hints:   (,,,,,,)   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,)   (,,,,,,)   (,,,,,,)

Proof of Theorem bnj571
StepHypRef Expression
1 nfv 1629 . . . 4
2 bnj571.17 . . . . 5
3 nfv 1629 . . . . . 6
4 nfv 1629 . . . . . 6
5 bnj571.30 . . . . . . 7
6 nfra1 2748 . . . . . . 7
75, 6nfxfr 1579 . . . . . 6
83, 4, 7nf3an 1849 . . . . 5
92, 8nfxfr 1579 . . . 4
10 nfv 1629 . . . 4
111, 9, 10nf3an 1849 . . 3
12 df-bnj17 28988 . . . . . . . . 9
13 3anass 940 . . . . . . . . . 10
14 3anrot 941 . . . . . . . . . 10
15 bnj571.20 . . . . . . . . . . . 12
16 df-3an 938 . . . . . . . . . . . 12
1715, 16bitri 241 . . . . . . . . . . 11
1817anbi2i 676 . . . . . . . . . 10
1913, 14, 183bitr4ri 270 . . . . . . . . 9
2012, 19bitri 241 . . . . . . . 8
21 bnj571.3 . . . . . . . . 9
22 bnj571.16 . . . . . . . . 9
23 bnj571.18 . . . . . . . . 9
24 bnj571.19 . . . . . . . . 9
25 bnj571.22 . . . . . . . . 9
26 bnj571.23 . . . . . . . . 9
27 bnj571.24 . . . . . . . . 9
28 bnj571.25 . . . . . . . . 9
29 bnj571.26 . . . . . . . . 9
30 bnj571.29 . . . . . . . . 9
31 bnj571.38 . . . . . . . . 9
3221, 22, 2, 23, 24, 15, 25, 26, 27, 28, 29, 30, 5, 31bnj558 29210 . . . . . . . 8
3320, 32sylbir 205 . . . . . . 7
34333expib 1156 . . . . . 6
35 df-bnj17 28988 . . . . . . . . 9
36 3anass 940 . . . . . . . . . 10
37 3anrot 941 . . . . . . . . . 10
38 bnj571.21 . . . . . . . . . . . 12
39 df-3an 938 . . . . . . . . . . . 12
4038, 39bitri 241 . . . . . . . . . . 11
4140anbi2i 676 . . . . . . . . . 10
4236, 37, 413bitr4ri 270 . . . . . . . . 9
4335, 42bitri 241 . . . . . . . 8
44 bnj571.40 . . . . . . . . 9
4521, 2, 24, 38, 27, 22, 44, 5bnj570 29213 . . . . . . . 8
4643, 45sylbir 205 . . . . . . 7
47463expib 1156 . . . . . 6
4834, 47pm2.61ine 2674 . . . . 5
4948, 27syl6eq 2483 . . . 4
5049exp32 589 . . 3
5111, 50alrimi 1781 . 2
52 bnj571.33 . . 3
5352bnj946 29082 . 2
5451, 53sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wal 1549   wceq 1652   wcel 1725   wne 2598  wral 2697   cdif 3309   cun 3310  c0 3620  csn 3806  cop 3809  ciun 4085   csuc 4575  com 4837   wfn 5441  cfv 5446   w-bnj17 28987   c-bnj14 28989   w-bnj15 28993 This theorem is referenced by:  bnj600  29227  bnj908  29239 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693  ax-reg 7552 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-tr 4295  df-eprel 4486  df-id 4490  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577  df-lim 4578  df-suc 4579  df-om 4838  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-res 4882  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454  df-bnj17 28988
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