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Theorem bnj966 32956
 Description: Technical lemma for bnj69 33020. 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
bnj966.3
bnj966.10
bnj966.12
bnj966.13
bnj966.44
bnj966.53
Assertion
Ref Expression
bnj966
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)

Proof of Theorem bnj966
StepHypRef Expression
1 bnj966.53 . . . . . 6
21bnj930 32782 . . . . 5
323adant3 1011 . . . 4
4 opex 4704 . . . . . . 7
54snid 4048 . . . . . 6
6 elun2 3665 . . . . . 6
75, 6ax-mp 5 . . . . 5
8 bnj966.13 . . . . 5
97, 8eleqtrri 2547 . . . 4
10 funopfv 5898 . . . 4
113, 9, 10mpisyl 18 . . 3
12 simp22 1025 . . . 4
13 simp33 1029 . . . . 5
14 bnj551 32753 . . . . 5
1512, 13, 14syl2anc 661 . . . 4
16 suceq 4936 . . . . . . . 8
1716eqeq2d 2474 . . . . . . 7
1817biimpac 486 . . . . . 6
1918fveq2d 5861 . . . . 5
20 bnj966.12 . . . . . . 7
21 fveq2 5857 . . . . . . . 8
2221bnj1113 32798 . . . . . . 7
2320, 22syl5eq 2513 . . . . . 6
2423adantl 466 . . . . 5
2519, 24eqeq12d 2482 . . . 4
2612, 15, 25syl2anc 661 . . 3
2711, 26mpbid 210 . 2
28 bnj966.44 . . . . . 6
29283adant3 1011 . . . . 5
30 bnj966.3 . . . . . . . 8
3130bnj1235 32817 . . . . . . 7
32313ad2ant1 1012 . . . . . 6
33323ad2ant2 1013 . . . . 5
34 simp23 1026 . . . . 5
3529, 33, 34, 13bnj951 32788 . . . 4
36 bnj966.10 . . . . . . . . 9
3736bnj923 32780 . . . . . . . 8
3830, 37bnj769 32774 . . . . . . 7
39383ad2ant1 1012 . . . . . 6
40 simp3 993 . . . . . 6
4139, 40bnj240 32706 . . . . 5
42 vex 3109 . . . . . . 7
4342bnj216 32742 . . . . . 6
4443adantl 466 . . . . 5
4541, 44syl 16 . . . 4
46 bnj658 32762 . . . . . . 7
4746anim1i 568 . . . . . 6
48 df-bnj17 32694 . . . . . 6
4947, 48sylibr 212 . . . . 5
508bnj945 32786 . . . . 5
5149, 50syl 16 . . . 4
5235, 45, 51syl2anc 661 . . 3
5320, 8bnj958 32952 . . . . 5
5453bnj956 32789 . . . 4
5554eqeq2d 2474 . . 3
5652, 55syl 16 . 2
5727, 56mpbird 232 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 968   wceq 1374   wcel 1762  cvv 3106   cdif 3466   cun 3467  c0 3778  csn 4020  cop 4026  ciun 4318   csuc 4873   wfun 5573   wfn 5574  cfv 5579  com 6671   w-bnj17 32693   c-bnj14 32695   w-bnj15 32699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-8 1764  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-sep 4561  ax-nul 4569  ax-pr 4679  ax-un 6567  ax-reg 8007 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2272  df-mo 2273  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3108  df-sbc 3325  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-if 3933  df-sn 4021  df-pr 4023  df-op 4027  df-uni 4239  df-iun 4320  df-br 4441  df-opab 4499  df-eprel 4784  df-id 4788  df-fr 4831  df-suc 4877  df-xp 4998  df-rel 4999  df-cnv 5000  df-co 5001  df-dm 5002  df-res 5004  df-iota 5542  df-fun 5581  df-fn 5582  df-fv 5587  df-bnj17 32694 This theorem is referenced by:  bnj910  32960
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