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Theorem bnj938 29757
 Description: Technical lemma for bnj69 29828. 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
bnj938.1
bnj938.2
bnj938.3
bnj938.4
bnj938.5
Assertion
Ref Expression
bnj938
Distinct variable groups:   ,,,   ,,,   ,,,   ,,
Allowed substitution hints:   (,,,,,)   (,,,,,)   (,,)   (,,,,,)   (,,)   (,,,,,)   (,,,,,)   (,,,,,)

Proof of Theorem bnj938
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elisset 3091 . . 3
21bnj706 29573 . 2
3 bnj291 29525 . . . . . 6
43simplbi 461 . . . . 5
5 bnj602 29735 . . . . . . . . . 10
65eqeq2d 2436 . . . . . . . . 9
7 bnj938.4 . . . . . . . . 9
86, 7syl6bbr 266 . . . . . . . 8
983anbi2d 1340 . . . . . . 7
10 bnj938.2 . . . . . . 7
119, 10syl6bbr 266 . . . . . 6
12113anbi2d 1340 . . . . 5
134, 12syl5ibr 224 . . . 4
14 bnj938.1 . . . . 5
15 biid 239 . . . . 5
16 bnj938.3 . . . . 5
17 biid 239 . . . . 5
18 bnj938.5 . . . . 5
1914, 15, 16, 17, 18bnj546 29716 . . . 4
2013, 19syl6 34 . . 3
2120exlimiv 1770 . 2
222, 21mpcom 37 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   w3a 982   wceq 1437  wex 1657   wcel 1872  wral 2771  cvv 3080   cdif 3433  c0 3761  csn 3998  ciun 4299   csuc 5444   wfn 5596  cfv 5601  com 6707   w-bnj17 29500   c-bnj14 29502   w-bnj15 29506 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-rep 4536  ax-sep 4546  ax-nul 4555  ax-pr 4660  ax-un 6598 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2273  df-mo 2274  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-ral 2776  df-rex 2777  df-reu 2778  df-rab 2780  df-v 3082  df-sbc 3300  df-csb 3396  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-pss 3452  df-nul 3762  df-if 3912  df-pw 3983  df-sn 3999  df-pr 4001  df-tp 4003  df-op 4005  df-uni 4220  df-iun 4301  df-br 4424  df-opab 4483  df-mpt 4484  df-tr 4519  df-eprel 4764  df-id 4768  df-po 4774  df-so 4775  df-fr 4812  df-we 4814  df-xp 4859  df-rel 4860  df-cnv 4861  df-co 4862  df-dm 4863  df-rn 4864  df-res 4865  df-ima 4866  df-ord 5445  df-on 5446  df-lim 5447  df-suc 5448  df-iota 5565  df-fun 5603  df-fn 5604  df-f 5605  df-f1 5606  df-fo 5607  df-f1o 5608  df-fv 5609  df-om 6708  df-bnj17 29501  df-bnj14 29503  df-bnj13 29505  df-bnj15 29507 This theorem is referenced by:  bnj944  29758  bnj969  29766
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