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Theorem bnj557 33047
 Description: Technical lemma for bnj852 33067. 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
bnj557.3
bnj557.16
bnj557.17
bnj557.18
bnj557.19
bnj557.20
bnj557.21
bnj557.22
bnj557.23
bnj557.24
bnj557.25
bnj557.28
bnj557.29
bnj557.36
Assertion
Ref Expression
bnj557
Distinct variable groups:   ,,,   ,   ,,,   ,,,   ,,   ,
Allowed substitution hints:   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,)   (,,,,,,)

Proof of Theorem bnj557
StepHypRef Expression
1 df-bnj17 32828 . . . . . 6
2 bnj256 32847 . . . . . 6
31, 2bitr3i 251 . . . . 5
4 bnj557.18 . . . . . . . 8
5 bnj557.19 . . . . . . . 8
64, 5bnj556 33046 . . . . . . 7
763anim3i 1184 . . . . . 6
8 bnj557.20 . . . . . . 7
9 vex 3116 . . . . . . . 8
109bnj216 32876 . . . . . . 7
118, 10bnj837 32907 . . . . . 6
127, 11anim12i 566 . . . . 5
133, 12sylbir 213 . . . 4
145bnj1254 32956 . . . . . 6
158simp3bi 1013 . . . . . 6
16 bnj551 32887 . . . . . 6
1714, 15, 16syl2an 477 . . . . 5
1817adantl 466 . . . 4
1913, 18jca 532 . . 3
20 df-3an 975 . . 3
2119, 2, 203imtr4i 266 . 2
22 bnj557.28 . . 3
23 bnj557.29 . . 3
24 bnj557.3 . . 3
25 bnj557.16 . . 3
26 bnj557.17 . . 3
27 bnj557.22 . . 3
28 bnj557.25 . . 3
29 bnj557.21 . . 3
30 bnj557.23 . . 3
31 bnj557.24 . . 3
32 bnj557.36 . . 3
3322, 23, 24, 25, 26, 4, 27, 28, 29, 30, 31, 32bnj553 33044 . 2
3421, 33syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1379   wcel 1767  wral 2814   cdif 3473   cun 3474  c0 3785  csn 4027  cop 4033  ciun 4325   csuc 4880   wfn 5582  cfv 5587  com 6679   w-bnj17 32827   c-bnj14 32829   w-bnj15 32833 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686  ax-un 6575  ax-reg 8017 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-sbc 3332  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-iun 4327  df-br 4448  df-opab 4506  df-eprel 4791  df-id 4795  df-fr 4838  df-suc 4884  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-res 5011  df-iota 5550  df-fun 5589  df-fn 5590  df-fv 5595  df-bnj17 32828 This theorem is referenced by:  bnj558  33048
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