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Theorem bnj998 29329
 Description: Technical lemma for bnj69 29381. 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
bnj998.1
bnj998.2
bnj998.3
bnj998.4
bnj998.5
bnj998.7
bnj998.8
bnj998.9
bnj998.10
bnj998.11
bnj998.12
bnj998.13
bnj998.14
bnj998.15
bnj998.16
Assertion
Ref Expression
bnj998
Distinct variable groups:   ,,,,,   ,,,   ,   ,,,,,   ,,,   ,,,   ,
Allowed substitution hints:   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,)   (,,,,,,)   (,,,,,,)   (,,,)   (,)   (,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)

Proof of Theorem bnj998
StepHypRef Expression
1 bnj998.4 . . . . . 6
2 bnj253 29070 . . . . . . 7
32simp1bi 973 . . . . . 6
41, 3sylbi 189 . . . . 5
54bnj705 29123 . . . 4
6 bnj643 29119 . . . 4
7 bnj998.5 . . . . . 6
8 3simpc 957 . . . . . 6
97, 8sylbi 189 . . . . 5
109bnj707 29125 . . . 4
11 bnj255 29071 . . . 4
125, 6, 10, 11syl3anbrc 1139 . . 3
13 bnj252 29069 . . 3
1412, 13sylib 190 . 2
15 bnj998.1 . . 3
16 bnj998.2 . . 3
17 bnj998.3 . . 3
18 bnj998.7 . . 3
19 bnj998.8 . . 3
20 bnj998.9 . . 3
21 bnj998.10 . . 3
22 bnj998.11 . . 3
23 bnj998.12 . . 3
24 bnj998.13 . . 3
25 bnj998.14 . . 3
26 bnj998.15 . . 3
27 bnj998.16 . . 3
28 biid 229 . . 3
29 biid 229 . . 3
3015, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29bnj910 29321 . 2
3114, 30syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726  cab 2424  wral 2707  wrex 2708  wsbc 3163   cdif 3319   cun 3320  c0 3630  csn 3816  cop 3819  ciun 4095   csuc 4585  com 4847   wfn 5451  cfv 5456   w-bnj17 29052   c-bnj14 29054   w-bnj15 29058   c-bnj18 29060 This theorem is referenced by:  bnj1020  29336 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4322  ax-sep 4332  ax-nul 4340  ax-pr 4405  ax-un 4703  ax-reg 7562 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-iun 4097  df-br 4215  df-opab 4269  df-mpt 4270  df-tr 4305  df-eprel 4496  df-id 4500  df-po 4505  df-so 4506  df-fr 4543  df-we 4545  df-ord 4586  df-on 4587  df-lim 4588  df-suc 4589  df-om 4848  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-f1 5461  df-fo 5462  df-f1o 5463  df-fv 5464  df-bnj17 29053  df-bnj14 29055  df-bnj13 29057  df-bnj15 29059
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