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Theorem bnj910 29767
 Description: Technical lemma for bnj69 29827. 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
bnj910.1
bnj910.2
bnj910.3
bnj910.4
bnj910.5
bnj910.6
bnj910.7
bnj910.8
bnj910.9
bnj910.10
bnj910.11
bnj910.12
bnj910.13
bnj910.14
bnj910.15
Assertion
Ref Expression
bnj910
Distinct variable groups:   ,,,,,   ,,,   ,   ,,,,,   ,,,   ,,,   ,
Allowed substitution hints:   (,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   ()   (,,,,,)   (,,,,,)   (,,)   ()   (,,,,)   (,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)

Proof of Theorem bnj910
StepHypRef Expression
1 bnj910.3 . . . 4
2 bnj910.10 . . . 4
31, 2bnj970 29766 . . 3
4 bnj910.1 . . . . 5
5 bnj910.2 . . . . 5
6 bnj910.12 . . . . 5
7 bnj910.14 . . . . 5
8 bnj910.15 . . . . 5
94, 5, 1, 2, 6, 7, 8bnj969 29765 . . . 4
10 simpr3 1013 . . . 4
111bnj1235 29624 . . . . . 6
12113ad2ant1 1026 . . . . 5
1312adantl 467 . . . 4
14 bnj910.13 . . . . . 6
1514bnj941 29592 . . . . 5
16153impib 1203 . . . 4
179, 10, 13, 16syl3anc 1264 . . 3
18 bnj910.4 . . . 4
19 bnj910.7 . . . 4
204, 5, 1, 18, 19, 2, 6, 14, 7, 8bnj944 29757 . . 3
21 bnj910.5 . . . 4
22 bnj910.8 . . . 4
235, 1, 2, 6, 14, 9bnj967 29764 . . . 4
241, 2, 6, 14, 9, 17bnj966 29763 . . . 4
255, 1, 21, 22, 6, 14, 23, 24bnj964 29762 . . 3
263, 17, 20, 25bnj951 29595 . 2
27 bnj910.6 . . . 4
28 vex 3083 . . . 4
291, 18, 21, 27, 28bnj919 29586 . . 3
30 bnj910.9 . . 3
3114bnj918 29585 . . 3
3229, 19, 22, 30, 31bnj976 29597 . 2
3326, 32sylibr 215 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   w3a 982   wceq 1437   wcel 1872  cab 2407  wral 2771  wrex 2772  cvv 3080  wsbc 3299   cdif 3433   cun 3434  c0 3761  csn 3998  cop 4004  ciun 4299   csuc 5444   wfn 5596  cfv 5601  com 6706   w-bnj17 29499   c-bnj14 29501   w-bnj15 29505 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-rep 4536  ax-sep 4546  ax-nul 4555  ax-pr 4660  ax-un 6597  ax-reg 8116 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2273  df-mo 2274  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-ral 2776  df-rex 2777  df-reu 2778  df-rab 2780  df-v 3082  df-sbc 3300  df-csb 3396  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-pss 3452  df-nul 3762  df-if 3912  df-pw 3983  df-sn 3999  df-pr 4001  df-tp 4003  df-op 4005  df-uni 4220  df-iun 4301  df-br 4424  df-opab 4483  df-mpt 4484  df-tr 4519  df-eprel 4764  df-id 4768  df-po 4774  df-so 4775  df-fr 4812  df-we 4814  df-xp 4859  df-rel 4860  df-cnv 4861  df-co 4862  df-dm 4863  df-rn 4864  df-res 4865  df-ima 4866  df-ord 5445  df-on 5446  df-lim 5447  df-suc 5448  df-iota 5565  df-fun 5603  df-fn 5604  df-f 5605  df-f1 5606  df-fo 5607  df-f1o 5608  df-fv 5609  df-om 6707  df-bnj17 29500  df-bnj14 29502  df-bnj13 29504  df-bnj15 29506 This theorem is referenced by:  bnj998  29775
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