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Theorem bnj153 29152
 Description: Technical lemma for bnj852 29193. 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
bnj153.1
bnj153.2
bnj153.3
bnj153.4
bnj153.5
Assertion
Ref Expression
bnj153
Distinct variable groups:   ,,,,,   ,,,,,   ,
Allowed substitution hints:   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   ()   (,,,,,)   ()

Proof of Theorem bnj153
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj153.1 . 2
2 bnj153.2 . 2
3 bnj153.3 . 2
4 bnj153.4 . 2
5 bnj153.5 . 2
6 biid 228 . 2
7 biid 228 . . . 4
81, 7bnj118 29141 . . 3
98bicomi 194 . 2
10 bnj105 28990 . . . 4
112, 10bnj92 29134 . . 3
1211bicomi 194 . 2
13 biid 228 . 2
14 biid 228 . 2
15 biid 228 . 2
16 biid 228 . . . . 5
17 biid 228 . . . . 5
186, 16, 7, 17bnj121 29142 . . . 4
198anbi2i 676 . . . . . . 7
2019, 11anbi12i 679 . . . . . 6
21 df-3an 938 . . . . . 6
22 df-3an 938 . . . . . 6
2320, 21, 223bitr4i 269 . . . . 5
2423imbi2i 304 . . . 4
2518, 24bitri 241 . . 3
2625bicomi 194 . 2
27 eqid 2435 . 2
28 biid 228 . 2
29 biid 228 . 2
3026sbcbii 3208 . . 3
31 biid 228 . . . . 5
32 biid 228 . . . . 5
33 biid 228 . . . . 5
3427, 31, 32, 33, 18bnj124 29143 . . . 4
351, 7, 31, 27bnj125 29144 . . . . . . . 8
3635anbi2i 676 . . . . . . 7
372, 17, 32, 27bnj126 29145 . . . . . . 7
3836, 37anbi12i 679 . . . . . 6
39 df-3an 938 . . . . . 6
40 df-3an 938 . . . . . 6
4138, 39, 403bitr4i 269 . . . . 5
4241imbi2i 304 . . . 4
4334, 42bitri 241 . . 3
4430, 43bitr2i 242 . 2
45 biid 228 . 2
46 biid 228 . . . . 5
47 biid 228 . . . . 5
48 biid 228 . . . . 5
49 biid 228 . . . . 5
5046, 47, 48, 49bnj156 28996 . . . 4
5148, 8bnj154 29150 . . . . . . 7
5251anbi2i 676 . . . . . 6
5317, 11bitri 241 . . . . . . 7
5449, 53bnj155 29151 . . . . . 6
5552, 54anbi12i 679 . . . . 5
56 df-3an 938 . . . . 5
57 df-3an 938 . . . . 5
5855, 56, 573bitr4i 269 . . . 4
5950, 58bitri 241 . . 3
6023sbcbii 3208 . . 3
6159, 60bitr3i 243 . 2
62 biid 228 . 2
63 biid 228 . 2
641, 2, 3, 4, 5, 6, 9, 12, 13, 14, 15, 26, 27, 28, 29, 44, 45, 61, 62, 63bnj151 29149 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  weu 2280  wmo 2281  wral 2697  wsbc 3153   cdif 3309  c0 3620  csn 3806  cop 3809  ciun 4085   class class class wbr 4204   cep 4484   csuc 4575  com 4837   wfn 5441  cfv 5446  c1o 6709   c-bnj14 28953   w-bnj15 28957 This theorem is referenced by:  bnj852  29193 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 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-suc 4579  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453  df-fv 5454  df-1o 6716  df-bnj13 28956  df-bnj15 28958
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