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Theorem bnj1015 34120
 Description: Technical lemma for bnj69 34167. 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
bnj1015.1
bnj1015.2
bnj1015.13
bnj1015.14
bnj1015.15
bnj1015.16
Assertion
Ref Expression
bnj1015
Distinct variable groups:   ,,,,   ,   ,,,,   ,,,,   ,
Allowed substitution hints:   (,,)   (,,,)   (,,,)   (,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1015
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1015.16 . . 3
21elexi 3119 . 2
3 eleq1 2529 . . . 4
43anbi2d 703 . . 3
5 fveq2 5872 . . . 4
65sseq1d 3526 . . 3
74, 6imbi12d 320 . 2
8 bnj1015.15 . . . 4
98elexi 3119 . . 3
10 eleq1 2529 . . . . 5
11 dmeq 5213 . . . . . 6
1211eleq2d 2527 . . . . 5
1310, 12anbi12d 710 . . . 4
14 fveq1 5871 . . . . 5
1514sseq1d 3526 . . . 4
1613, 15imbi12d 320 . . 3
17 bnj1015.1 . . . 4
18 bnj1015.2 . . . 4
19 bnj1015.13 . . . 4
20 bnj1015.14 . . . 4
2117, 18, 19, 20bnj1014 34119 . . 3
229, 16, 21vtocl 3161 . 2
232, 7, 22vtocl 3161 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1395   wcel 1819  cab 2442  wral 2807  wrex 2808   cdif 3468   wss 3471  c0 3793  csn 4032  ciun 4332   csuc 4889   cdm 5008   wfn 5589  cfv 5594  com 6699   c-bnj14 33841   c-bnj18 33847 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-iun 4334  df-br 4457  df-dm 5018  df-iota 5557  df-fv 5602  df-bnj18 33848 This theorem is referenced by:  bnj1018  34121
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