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Theorem dicopelval 34816
 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 34815 . . 3
98eleq2d 2534 . 2
10 dicelval.f . . 3
11 dicelval.s . . 3
12 eqeq1 2475 . . . 4
1312anbi1d 719 . . 3
14 fveq1 5878 . . . . 5
1514eqeq2d 2481 . . . 4
16 eleq1 2537 . . . 4
1715, 16anbi12d 725 . . 3
1810, 11, 13, 17opelopab 4723 . 2
199, 18syl6bb 269 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189   wa 376   wceq 1452   wcel 1904  cvv 3031  cop 3965   class class class wbr 4395  copab 4453  cfv 5589  crio 6269  cple 15275  coc 15276  catm 32900  clh 33620  cltrn 33737  ctendo 34390  cdic 34811 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-rep 4508  ax-sep 4518  ax-nul 4527  ax-pow 4579  ax-pr 4639  ax-un 6602 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-reu 2763  df-rab 2765  df-v 3033  df-sbc 3256  df-csb 3350  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-pw 3944  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-iun 4271  df-br 4396  df-opab 4455  df-mpt 4456  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-rn 4850  df-res 4851  df-ima 4852  df-iota 5553  df-fun 5591  df-fn 5592  df-f 5593  df-f1 5594  df-fo 5595  df-f1o 5596  df-fv 5597  df-riota 6270  df-dic 34812 This theorem is referenced by:  dicopelval2  34820  dicvaddcl  34829  dicvscacl  34830  dicn0  34831
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