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Theorem bnj1311 28427
 Description: Technical lemma for bnj60 28465. 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
bnj1311.1
bnj1311.2
bnj1311.3
bnj1311.4
Assertion
Ref Expression
bnj1311
Distinct variable groups:   ,,,   ,,   ,,   ,,   ,,,   ,,   ,,,   ,   ,   ,   ,
Allowed substitution hints:   (,)   (,)   (,,,,)   (,,)   (,)   ()   (,,)

Proof of Theorem bnj1311
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 biid 227 . . . . . . . 8
21bnj1232 28209 . . . . . . 7
3 ssrab2 3258 . . . . . . . 8
4 bnj1311.4 . . . . . . . . 9
51bnj1235 28210 . . . . . . . . . . 11
6 bnj1311.2 . . . . . . . . . . . 12
7 bnj1311.3 . . . . . . . . . . . 12
8 eqid 2283 . . . . . . . . . . . 12
9 eqid 2283 . . . . . . . . . . . 12
106, 7, 8, 9bnj1234 28416 . . . . . . . . . . 11
115, 10syl6eleq 2373 . . . . . . . . . 10
12 abid 2271 . . . . . . . . . . . . . 14
1312bnj1238 28212 . . . . . . . . . . . . 13
1413bnj1196 28200 . . . . . . . . . . . 12
15 bnj1311.1 . . . . . . . . . . . . . . 15
1615abeq2i 2390 . . . . . . . . . . . . . 14
1716simplbi 446 . . . . . . . . . . . . 13
18 fndm 5343 . . . . . . . . . . . . 13
1917, 18bnj1241 28213 . . . . . . . . . . . 12
2014, 19bnj593 28147 . . . . . . . . . . 11
2120bnj937 28176 . . . . . . . . . 10
22 ssinss1 3397 . . . . . . . . . 10
2311, 21, 223syl 18 . . . . . . . . 9
244, 23syl5eqss 3222 . . . . . . . 8
253, 24syl5ss 3190 . . . . . . 7
26 eqid 2283 . . . . . . . 8
27 biid 227 . . . . . . . 8
2815, 6, 7, 4, 26, 1, 27bnj1253 28420 . . . . . . 7
29 nfrab1 2720 . . . . . . . . 9
3029nfcrii 2412 . . . . . . . 8
3130bnj1228 28414 . . . . . . 7
322, 25, 28, 31syl3anc 1182 . . . . . 6
33 ax-17 1603 . . . . . . 7
3415bnj1309 28425 . . . . . . . . . 10
357, 34bnj1307 28426 . . . . . . . . 9
3635nfcii 2410 . . . . . . . 8
3736nfcrii 2412 . . . . . . 7
3836nfcrii 2412 . . . . . . 7
39 ax-17 1603 . . . . . . 7
4033, 37, 38, 39bnj982 28183 . . . . . 6
4132, 27, 40bnj1521 28256 . . . . 5
42 simp2 956 . . . . 5
4315, 6, 7, 4, 26, 1, 27bnj1279 28421 . . . . . . . . 9
44433adant1 973 . . . . . . . 8
4515, 6, 7, 4, 26, 1, 27, 44bnj1280 28423 . . . . . . 7
46 eqid 2283 . . . . . . 7
47 eqid 2283 . . . . . . 7
4815, 6, 7, 4, 26, 1, 27, 45, 8, 9, 46, 47bnj1296 28424 . . . . . 6
4926bnj1538 28260 . . . . . . 7
5049necon2bi 2492 . . . . . 6
5148, 50syl 15 . . . . 5
5241, 42, 51bnj1304 28225 . . . 4
53 df-bnj17 28085 . . . 4
5452, 53mtbi 289 . . 3
5554imnani 412 . 2
56 nne 2450 . 2
5755, 56sylib 188 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358   w3a 934   wceq 1623   wcel 1684  cab 2269   wne 2446  wral 2543  wrex 2544  crab 2547   cin 3151   wss 3152  c0 3455  cop 3643   class class class wbr 4023   cdm 4689   cres 4691   wfn 5250  cfv 5255   w-bnj17 28084   c-bnj14 28086   w-bnj15 28090 This theorem is referenced by:  bnj1326  28429  bnj60  28465 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-rep 4131  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214  ax-un 4512  ax-reg 7306  ax-inf2 7342 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-reu 2550  df-rab 2552  df-v 2790  df-sbc 2992  df-csb 3082  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-pss 3168  df-nul 3456  df-if 3566  df-pw 3627  df-sn 3646  df-pr 3647  df-tp 3648  df-op 3649  df-uni 3828  df-iun 3907  df-br 4024  df-opab 4078  df-mpt 4079  df-tr 4114  df-eprel 4305  df-id 4309  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395  df-on 4396  df-lim 4397  df-suc 4398  df-om 4657  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fn 5258  df-f 5259  df-f1 5260  df-fo 5261  df-f1o 5262  df-fv 5263  df-1o 6479  df-bnj17 28085  df-bnj14 28087  df-bnj13 28089  df-bnj15 28091  df-bnj18 28093  df-bnj19 28095
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