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Theorem bnj966 29757
 Description: Technical lemma for bnj69 29821. 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 29583 . . . . 5
323adant3 1026 . . . 4
4 opex 4683 . . . . . . 7
54snid 4025 . . . . . 6
6 elun2 3635 . . . . . 6
75, 6ax-mp 5 . . . . 5
8 bnj966.13 . . . . 5
97, 8eleqtrri 2510 . . . 4
10 funopfv 5918 . . . 4
113, 9, 10mpisyl 22 . . 3
12 simp22 1040 . . . 4
13 simp33 1044 . . . . 5
14 bnj551 29554 . . . . 5
1512, 13, 14syl2anc 666 . . . 4
16 suceq 5505 . . . . . . . 8
1716eqeq2d 2437 . . . . . . 7
1817biimpac 489 . . . . . 6
1918fveq2d 5883 . . . . 5
20 bnj966.12 . . . . . . 7
21 fveq2 5879 . . . . . . . 8
2221bnj1113 29599 . . . . . . 7
2320, 22syl5eq 2476 . . . . . 6
2423adantl 468 . . . . 5
2519, 24eqeq12d 2445 . . . 4
2612, 15, 25syl2anc 666 . . 3
2711, 26mpbid 214 . 2
28 bnj966.44 . . . . . 6
29283adant3 1026 . . . . 5
30 bnj966.3 . . . . . . . 8
3130bnj1235 29618 . . . . . . 7
32313ad2ant1 1027 . . . . . 6
33323ad2ant2 1028 . . . . 5
34 simp23 1041 . . . . 5
3529, 33, 34, 13bnj951 29589 . . . 4
36 bnj966.10 . . . . . . . . 9
3736bnj923 29581 . . . . . . . 8
3830, 37bnj769 29575 . . . . . . 7
39383ad2ant1 1027 . . . . . 6
40 simp3 1008 . . . . . 6
4139, 40bnj240 29506 . . . . 5
42 vex 3085 . . . . . . 7
4342bnj216 29542 . . . . . 6
4443adantl 468 . . . . 5
4541, 44syl 17 . . . 4
46 bnj658 29563 . . . . . . 7
4746anim1i 571 . . . . . 6
48 df-bnj17 29494 . . . . . 6
4947, 48sylibr 216 . . . . 5
508bnj945 29587 . . . . 5
5149, 50syl 17 . . . 4
5235, 45, 51syl2anc 666 . . 3
5320, 8bnj958 29753 . . . . 5
5453bnj956 29590 . . . 4
5554eqeq2d 2437 . . 3
5652, 55syl 17 . 2
5727, 56mpbird 236 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   w3a 983   wceq 1438   wcel 1869  cvv 3082   cdif 3434   cun 3435  c0 3762  csn 3997  cop 4003  ciun 4297   csuc 5442   wfun 5593   wfn 5594  cfv 5599  com 6704   w-bnj17 29493   c-bnj14 29495   w-bnj15 29499 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-8 1871  ax-9 1873  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401  ax-sep 4544  ax-nul 4553  ax-pr 4658  ax-un 6595  ax-reg 8111 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-eu 2270  df-mo 2271  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-ral 2781  df-rex 2782  df-rab 2785  df-v 3084  df-sbc 3301  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-op 4004  df-uni 4218  df-iun 4299  df-br 4422  df-opab 4481  df-eprel 4762  df-id 4766  df-fr 4810  df-xp 4857  df-rel 4858  df-cnv 4859  df-co 4860  df-dm 4861  df-res 4863  df-suc 5446  df-iota 5563  df-fun 5601  df-fn 5602  df-fv 5607  df-bnj17 29494 This theorem is referenced by:  bnj910  29761
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