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Theorem bnj969 33484
 Description: Technical lemma for bnj69 33546. 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
bnj969.1
bnj969.2
bnj969.3
bnj969.10
bnj969.12
bnj969.14
bnj969.15
Assertion
Ref Expression
bnj969
Distinct variable groups:   ,,,   ,,,   ,,,   ,,
Allowed substitution hints:   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,)   (,,,,,)   (,,,,,)   (,,)   (,,,,,)

Proof of Theorem bnj969
StepHypRef Expression
1 simpl 457 . . . 4
2 bnj667 33289 . . . . . . 7
3 bnj969.3 . . . . . . 7
4 bnj969.14 . . . . . . 7
52, 3, 43imtr4i 266 . . . . . 6
653ad2ant1 1017 . . . . 5
76adantl 466 . . . 4
83bnj1232 33342 . . . . . . 7
9 vex 3121 . . . . . . . 8
109bnj216 33268 . . . . . . 7
11 id 22 . . . . . . 7
128, 10, 113anim123i 1181 . . . . . 6
13 bnj969.15 . . . . . . 7
14 3ancomb 982 . . . . . . 7
1513, 14bitri 249 . . . . . 6
1612, 15sylibr 212 . . . . 5
1716adantl 466 . . . 4
181, 7, 17jca32 535 . . 3
19 bnj256 33239 . . 3
2018, 19sylibr 212 . 2
21 bnj969.12 . . 3
22 bnj969.10 . . . 4
23 bnj969.1 . . . 4
24 bnj969.2 . . . 4
2522, 4, 13, 23, 24bnj938 33475 . . 3
2621, 25syl5eqel 2559 . 2
2720, 26syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1379   wcel 1767  wral 2817  cvv 3118   cdif 3478  c0 3790  csn 4033  ciun 4331   csuc 4886   wfn 5589  cfv 5594  com 6695   w-bnj17 33219   c-bnj14 33221   w-bnj15 33225 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-rep 4564  ax-sep 4574  ax-nul 4582  ax-pr 4692  ax-un 6587 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  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 2822  df-rex 2823  df-reu 2824  df-rab 2826  df-v 3120  df-sbc 3337  df-csb 3441  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-pss 3497  df-nul 3791  df-if 3946  df-pw 4018  df-sn 4034  df-pr 4036  df-tp 4038  df-op 4040  df-uni 4252  df-iun 4333  df-br 4454  df-opab 4512  df-mpt 4513  df-tr 4547  df-eprel 4797  df-id 4801  df-po 4806  df-so 4807  df-fr 4844  df-we 4846  df-ord 4887  df-on 4888  df-lim 4889  df-suc 4890  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-rn 5016  df-res 5017  df-ima 5018  df-iota 5557  df-fun 5596  df-fn 5597  df-f 5598  df-f1 5599  df-fo 5600  df-f1o 5601  df-fv 5602  df-om 6696  df-bnj17 33220  df-bnj14 33222  df-bnj13 33224  df-bnj15 33226 This theorem is referenced by:  bnj910  33486  bnj1006  33497
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