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Theorem diaval 31515
 Description: The partial isomorphism A for a lattice . Definition of isomorphism map in [Crawley] p. 120 line 24. (Contributed by NM, 15-Oct-2013.)
Hypotheses
Ref Expression
diaval.b
diaval.l
diaval.h
diaval.t
diaval.r
diaval.i
Assertion
Ref Expression
diaval
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()   ()

Proof of Theorem diaval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 diaval.b . . . . 5
2 diaval.l . . . . 5
3 diaval.h . . . . 5
4 diaval.t . . . . 5
5 diaval.r . . . . 5
6 diaval.i . . . . 5
71, 2, 3, 4, 5, 6diafval 31514 . . . 4
98fveq1d 5689 . 2
10 simpr 448 . . . 4
11 breq1 4175 . . . . 5
1211elrab 3052 . . . 4
1310, 12sylibr 204 . . 3
14 breq2 4176 . . . . 5
1514rabbidv 2908 . . . 4
16 eqid 2404 . . . 4
17 fvex 5701 . . . . . 6
184, 17eqeltri 2474 . . . . 5
1918rabex 4314 . . . 4
2015, 16, 19fvmpt 5765 . . 3
2113, 20syl 16 . 2
229, 21eqtrd 2436 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1649   wcel 1721  crab 2670  cvv 2916   class class class wbr 4172   cmpt 4226  cfv 5413  cbs 13424  cple 13491  clh 30466  cltrn 30583  ctrl 30640  cdia 31511 This theorem is referenced by:  diaelval  31516  diass  31525  diaord  31530  dia0  31535  dia1N  31536  diassdvaN  31543  dia1dim  31544  cdlemm10N  31601  dibval3N  31629  dihwN  31772 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-rep 4280  ax-sep 4290  ax-nul 4298  ax-pr 4363 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-reu 2673  df-rab 2675  df-v 2918  df-sbc 3122  df-csb 3212  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-iun 4055  df-br 4173  df-opab 4227  df-mpt 4228  df-id 4458  df-xp 4843  df-rel 4844  df-cnv 4845  df-co 4846  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850  df-iota 5377  df-fun 5415  df-fn 5416  df-f 5417  df-f1 5418  df-fo 5419  df-f1o 5420  df-fv 5421  df-disoa 31512
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