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Theorem dicopelval 31912
 Description: Membership in value of the partial isomorphism C for a lattice . (Contributed by NM, 15-Feb-2014.)
Hypotheses
Ref Expression
dicval.l
dicval.a
dicval.h
dicval.p
dicval.t
dicval.e
dicval.i
dicelval.f
dicelval.s
Assertion
Ref Expression
dicopelval
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()   ()   ()   ()   ()

Proof of Theorem dicopelval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dicval.l . . . 4
2 dicval.a . . . 4
3 dicval.h . . . 4
4 dicval.p . . . 4
5 dicval.t . . . 4
6 dicval.e . . . 4
7 dicval.i . . . 4
81, 2, 3, 4, 5, 6, 7dicval 31911 . . 3
98eleq2d 2502 . 2
10 dicelval.f . . 3
11 dicelval.s . . 3
12 eqeq1 2441 . . . 4
1312anbi1d 686 . . 3
14 fveq1 5719 . . . . 5
1514eqeq2d 2446 . . . 4
16 eleq1 2495 . . . 4
1715, 16anbi12d 692 . . 3
1810, 11, 13, 17opelopab 4468 . 2
199, 18syl6bb 253 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  cvv 2948  cop 3809   class class class wbr 4204  copab 4257  cfv 5446  crio 6534  cple 13528  coc 13529  catm 29998  clh 30718  cltrn 30835  ctendo 31486  cdic 31907 This theorem is referenced by:  dicopelval2  31916  dicvaddcl  31925  dicvscacl  31926  dicn0  31927 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-rep 4312  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693 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-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453  df-fv 5454  df-riota 6541  df-dic 31908
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