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Theorem bnj966 29252
 Description: Technical lemma for bnj69 29316. 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 29077 . . . . 5
323adant3 977 . . . 4
4 opex 4419 . . . . . . 7
54snid 3833 . . . . . 6
6 elun2 3507 . . . . . 6
75, 6ax-mp 8 . . . . 5
8 bnj966.13 . . . . 5
97, 8eleqtrri 2508 . . . 4
10 funopfv 5758 . . . 4
113, 9, 10ee10 1385 . . 3
12 simp22 991 . . . 4
13 simp33 995 . . . . 5
14 bnj551 29047 . . . . 5
1512, 13, 14syl2anc 643 . . . 4
16 suceq 4638 . . . . . . . 8
1716eqeq2d 2446 . . . . . . 7
1817biimpac 473 . . . . . 6
1918fveq2d 5724 . . . . 5
20 bnj966.12 . . . . . . 7
21 fveq2 5720 . . . . . . . 8
2221bnj1113 29093 . . . . . . 7
2320, 22syl5eq 2479 . . . . . 6
2423adantl 453 . . . . 5
2519, 24eqeq12d 2449 . . . 4
2612, 15, 25syl2anc 643 . . 3
2711, 26mpbid 202 . 2
28 bnj966.44 . . . . . 6
29283adant3 977 . . . . 5
30 bnj966.3 . . . . . . . 8
3130bnj1235 29113 . . . . . . 7
32313ad2ant1 978 . . . . . 6
33323ad2ant2 979 . . . . 5
34 simp23 992 . . . . 5
3529, 33, 34, 13bnj951 29083 . . . 4
36 bnj966.10 . . . . . . . . 9
3736bnj923 29074 . . . . . . . 8
3830, 37bnj769 29068 . . . . . . 7
39383ad2ant1 978 . . . . . 6
40 simp3 959 . . . . . 6
4139, 40bnj240 29000 . . . . 5
42 vex 2951 . . . . . . 7
4342bnj216 29036 . . . . . 6
4443adantl 453 . . . . 5
4541, 44syl 16 . . . 4
46 bnj658 29056 . . . . . . 7
4746anim1i 552 . . . . . 6
48 df-bnj17 28988 . . . . . 6
4947, 48sylibr 204 . . . . 5
508bnj945 29081 . . . . 5
5149, 50syl 16 . . . 4
5235, 45, 51syl2anc 643 . . 3
5320, 8bnj958 29248 . . . . 5
5453bnj956 29084 . . . 4
5554eqeq2d 2446 . . 3
5652, 55syl 16 . 2
5727, 56mpbird 224 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  cvv 2948   cdif 3309   cun 3310  c0 3620  csn 3806  cop 3809  ciun 4085   csuc 4575  com 4837   wfun 5440   wfn 5441  cfv 5446   w-bnj17 28987   c-bnj14 28989   w-bnj15 28993 This theorem is referenced by:  bnj910  29256 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-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-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-eprel 4486  df-id 4490  df-fr 4533  df-suc 4579  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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