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Theorem bnj998 32970
 Description: Technical lemma for bnj69 33022. 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 32713 . . . . . . 7
32simp1bi 1006 . . . . . 6
41, 3sylbi 195 . . . . 5
54bnj705 32766 . . . 4
6 bnj643 32762 . . . 4
7 bnj998.5 . . . . . 6
8 3simpc 990 . . . . . 6
97, 8sylbi 195 . . . . 5
109bnj707 32768 . . . 4
11 bnj255 32714 . . . 4
125, 6, 10, 11syl3anbrc 1175 . . 3
13 bnj252 32712 . . 3
1412, 13sylib 196 . 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 236 . . 3
29 biid 236 . . 3
3015, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29bnj910 32962 . 2
3114, 30syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 968   wceq 1374   wcel 1762  cab 2447  wral 2809  wrex 2810  wsbc 3326   cdif 3468   cun 3469  c0 3780  csn 4022  cop 4028  ciun 4320   csuc 4875   wfn 5576  cfv 5581  com 6673   w-bnj17 32695   c-bnj14 32697   w-bnj15 32701   c-bnj18 32703 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 1963  ax-ext 2440  ax-rep 4553  ax-sep 4563  ax-nul 4571  ax-pr 4681  ax-un 6569  ax-reg 8009 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 969  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2274  df-mo 2275  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ne 2659  df-ral 2814  df-rex 2815  df-reu 2816  df-rab 2818  df-v 3110  df-sbc 3327  df-csb 3431  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-pss 3487  df-nul 3781  df-if 3935  df-pw 4007  df-sn 4023  df-pr 4025  df-tp 4027  df-op 4029  df-uni 4241  df-iun 4322  df-br 4443  df-opab 4501  df-mpt 4502  df-tr 4536  df-eprel 4786  df-id 4790  df-po 4795  df-so 4796  df-fr 4833  df-we 4835  df-ord 4876  df-on 4877  df-lim 4878  df-suc 4879  df-xp 5000  df-rel 5001  df-cnv 5002  df-co 5003  df-dm 5004  df-rn 5005  df-res 5006  df-ima 5007  df-iota 5544  df-fun 5583  df-fn 5584  df-f 5585  df-f1 5586  df-fo 5587  df-f1o 5588  df-fv 5589  df-om 6674  df-bnj17 32696  df-bnj14 32698  df-bnj13 32700  df-bnj15 32702 This theorem is referenced by:  bnj1020  32977
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