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Theorem bnj150 29475
 Description: Technical lemma for bnj151 29476. 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
bnj150.1
bnj150.2
bnj150.3
bnj150.4
bnj150.5
bnj150.6
bnj150.7
bnj150.8
bnj150.9
bnj150.10
bnj150.11
Assertion
Ref Expression
bnj150
Distinct variable groups:   ,,,   ,,,   ,,,   ,   ,,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,)   (,)   (,)   (,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,)   (,,,,)

Proof of Theorem bnj150
StepHypRef Expression
1 0ex 4557 . . . . . . . . . 10
2 bnj93 29462 . . . . . . . . . 10
3 funsng 5647 . . . . . . . . . 10
41, 2, 3sylancr 667 . . . . . . . . 9
5 bnj150.8 . . . . . . . . . 10
65funeqi 5621 . . . . . . . . 9
74, 6sylibr 215 . . . . . . . 8
85bnj96 29464 . . . . . . . 8
97, 8bnj1422 29437 . . . . . . 7
105bnj97 29465 . . . . . . . 8
11 bnj150.1 . . . . . . . . 9
12 bnj150.4 . . . . . . . . 9
13 bnj150.9 . . . . . . . . 9
1411, 12, 13, 5bnj125 29471 . . . . . . . 8
1510, 14sylibr 215 . . . . . . 7
169, 15jca 534 . . . . . 6
17 bnj98 29466 . . . . . . 7
18 bnj150.2 . . . . . . . 8
19 bnj150.5 . . . . . . . 8
20 bnj150.10 . . . . . . . 8
2118, 19, 20, 5bnj126 29472 . . . . . . 7
2217, 21mpbir 212 . . . . . 6
2316, 22jctir 540 . . . . 5
24 df-3an 984 . . . . 5
2523, 24sylibr 215 . . . 4
26 bnj150.11 . . . . 5
27 bnj150.3 . . . . . 6
28 bnj150.7 . . . . . 6
2927, 28, 12, 19bnj121 29469 . . . . 5
305, 13, 20, 26, 29bnj124 29470 . . . 4
3125, 30mpbir 212 . . 3
325bnj95 29463 . . . 4
33 sbceq1a 3316 . . . . 5
3433, 26syl6bbr 266 . . . 4
3532, 34spcev 3179 . . 3
3631, 35ax-mp 5 . 2
37 bnj150.6 . . . 4
38 19.37v 1818 . . . 4
3937, 38bitr4i 255 . . 3
4039, 29bnj133 29321 . 2
4136, 40mpbir 212 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   w3a 982   wceq 1437  wex 1659   wcel 1870  wral 2782  cvv 3087  wsbc 3305  c0 3767  csn 4002  cop 4008  ciun 4302   csuc 5444   wfun 5595   wfn 5596  cfv 5601  com 6706  c1o 7183   c-bnj14 29281   w-bnj15 29285 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pow 4603  ax-pr 4661 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-sbc 3306  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-pw 3987  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-iun 4304  df-br 4427  df-opab 4485  df-id 4769  df-xp 4860  df-rel 4861  df-cnv 4862  df-co 4863  df-dm 4864  df-suc 5448  df-iota 5565  df-fun 5603  df-fn 5604  df-fv 5609  df-1o 7190  df-bnj13 29284  df-bnj15 29286 This theorem is referenced by:  bnj151  29476
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