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Theorem bnj1015 29269
 Description: Technical lemma for bnj69 29316. 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 2957 . 2
3 eleq1 2495 . . . 4
43anbi2d 685 . . 3
5 fveq2 5720 . . . 4
65sseq1d 3367 . . 3
74, 6imbi12d 312 . 2
8 bnj1015.15 . . . 4
98elexi 2957 . . 3
10 eleq1 2495 . . . . 5
11 dmeq 5062 . . . . . 6
1211eleq2d 2502 . . . . 5
1310, 12anbi12d 692 . . . 4
14 fveq1 5719 . . . . 5
1514sseq1d 3367 . . . 4
1613, 15imbi12d 312 . . 3
17 bnj1015.1 . . . 4
18 bnj1015.2 . . . 4
19 bnj1015.13 . . . 4
20 bnj1015.14 . . . 4
2117, 18, 19, 20bnj1014 29268 . . 3
229, 16, 21vtocl 2998 . 2
232, 7, 22vtocl 2998 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  cab 2421  wral 2697  wrex 2698   cdif 3309   wss 3312  c0 3620  csn 3806  ciun 4085   csuc 4575  com 4837   cdm 4870   wfn 5441  cfv 5446   c-bnj14 28989   c-bnj18 28995 This theorem is referenced by:  bnj1018  29270 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-dm 4880  df-iota 5410  df-fv 5454  df-bnj18 28996
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