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Theorem bnj150 29247
 Description: Technical lemma for bnj151 29248. 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 4339 . . . . . . . . . 10
2 bnj93 29234 . . . . . . . . . 10
3 funsng 5497 . . . . . . . . . 10
41, 2, 3sylancr 645 . . . . . . . . 9
5 bnj150.8 . . . . . . . . . 10
65funeqi 5474 . . . . . . . . 9
74, 6sylibr 204 . . . . . . . 8
85bnj96 29236 . . . . . . . 8
97, 8bnj1422 29209 . . . . . . 7
105bnj97 29237 . . . . . . . 8
11 bnj150.1 . . . . . . . . 9
12 bnj150.4 . . . . . . . . 9
13 bnj150.9 . . . . . . . . 9
1411, 12, 13, 5bnj125 29243 . . . . . . . 8
1510, 14sylibr 204 . . . . . . 7
169, 15jca 519 . . . . . 6
17 bnj98 29238 . . . . . . 7
18 bnj150.2 . . . . . . . 8
19 bnj150.5 . . . . . . . 8
20 bnj150.10 . . . . . . . 8
2118, 19, 20, 5bnj126 29244 . . . . . . 7
2217, 21mpbir 201 . . . . . 6
2316, 22jctir 525 . . . . 5
24 df-3an 938 . . . . 5
2523, 24sylibr 204 . . . 4
26 bnj150.11 . . . . 5
27 bnj150.3 . . . . . 6
28 bnj150.7 . . . . . 6
2927, 28, 12, 19bnj121 29241 . . . . 5
305, 13, 20, 26, 29bnj124 29242 . . . 4
3125, 30mpbir 201 . . 3
325bnj95 29235 . . . 4
33 sbceq1a 3171 . . . . 5
3433, 26syl6bbr 255 . . . 4
3532, 34spcev 3043 . . 3
3631, 35ax-mp 8 . 2
37 bnj150.6 . . . 4
38 19.37v 1922 . . . 4
3937, 38bitr4i 244 . . 3
4039, 29bnj133 29092 . 2
4136, 40mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  wral 2705  cvv 2956  wsbc 3161  c0 3628  csn 3814  cop 3817  ciun 4093   csuc 4583  com 4845   wfun 5448   wfn 5449  cfv 5454  c1o 6717   c-bnj14 29052   w-bnj15 29056 This theorem is referenced by:  bnj151  29248 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-id 4498  df-suc 4587  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-iota 5418  df-fun 5456  df-fn 5457  df-fv 5462  df-1o 6724  df-bnj13 29055  df-bnj15 29057
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