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Theorem bnj1384 33568
 Description: Technical lemma for bnj60 33598. 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
bnj1384.1
bnj1384.2
bnj1384.3
bnj1384.4
bnj1384.5
bnj1384.6
bnj1384.7
bnj1384.8
bnj1384.9
bnj1384.10
Assertion
Ref Expression
bnj1384
Distinct variable groups:   ,,,   ,   ,   ,,   ,,,   ,,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   ()   (,,)   (,,)   (,,,)   (,,,)   ()   (,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1384
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1384.1 . . . . 5
2 bnj1384.2 . . . . 5
3 bnj1384.3 . . . . 5
4 bnj1384.4 . . . . 5
5 bnj1384.5 . . . . 5
6 bnj1384.6 . . . . 5
7 bnj1384.7 . . . . 5
8 bnj1384.8 . . . . 5
9 bnj1384.9 . . . . 5
10 bnj1384.10 . . . . 5
111, 2, 3, 4, 8bnj1373 33566 . . . . 5
121, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11bnj1371 33565 . . . 4
1312rgen 2827 . . 3
14 id 22 . . . . . 6
151, 2, 3, 4, 5, 6, 7, 8, 9bnj1374 33567 . . . . . 6
16 nfab1 2631 . . . . . . . . . 10
179, 16nfcxfr 2627 . . . . . . . . 9
1817nfcri 2622 . . . . . . . 8
19 nfab1 2631 . . . . . . . . . 10
203, 19nfcxfr 2627 . . . . . . . . 9
2120nfcri 2622 . . . . . . . 8
2218, 21nfim 1867 . . . . . . 7
23 eleq1 2539 . . . . . . . 8
24 eleq1 2539 . . . . . . . 8
2523, 24imbi12d 320 . . . . . . 7
2622, 25, 15chvar 1982 . . . . . 6
27 eqid 2467 . . . . . . 7
281, 2, 3, 27bnj1326 33562 . . . . . 6
2914, 15, 26, 28syl3an 1270 . . . . 5
30293expib 1199 . . . 4
3130ralrimivv 2887 . . 3
32 biid 236 . . . 4
33 biid 236 . . . 4
349bnj1317 33360 . . . 4
3532, 27, 33, 34bnj1386 33372 . . 3
3613, 31, 35sylancr 663 . 2
3710funeqi 5614 . 2
3836, 37sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369   w3a 973   wceq 1379  wex 1596   wcel 1767  cab 2452   wne 2662  wral 2817  wrex 2818  crab 2821  wsbc 3336   cun 3479   cin 3480   wss 3481  c0 3790  csn 4033  cop 4039  cuni 4251   class class class wbr 4453   cdm 5005   cres 5007   wfun 5588   wfn 5589  cfv 5594   c-bnj14 33221   w-bnj15 33225   c-bnj18 33227 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-pow 4631  ax-pr 4692  ax-un 6587  ax-reg 8030  ax-inf2 8070 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1382  df-fal 1385  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-1o 7142  df-bnj17 33220  df-bnj14 33222  df-bnj13 33224  df-bnj15 33226  df-bnj18 33228  df-bnj19 33230 This theorem is referenced by:  bnj1312  33594
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