Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  diaelval Structured version   Unicode version

Theorem diaelval 31831
 Description: Member of the partial isomorphism A for a lattice . (Contributed by NM, 3-Dec-2013.)
Hypotheses
Ref Expression
diaval.b
diaval.l
diaval.h
diaval.t
diaval.r
diaval.i
Assertion
Ref Expression
diaelval

Proof of Theorem diaelval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 diaval.b . . . 4
2 diaval.l . . . 4
3 diaval.h . . . 4
4 diaval.t . . . 4
5 diaval.r . . . 4
6 diaval.i . . . 4
71, 2, 3, 4, 5, 6diaval 31830 . . 3
87eleq2d 2503 . 2
9 fveq2 5728 . . . 4
109breq1d 4222 . . 3
1110elrab 3092 . 2
128, 11syl6bb 253 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  crab 2709   class class class wbr 4212  cfv 5454  cbs 13469  cple 13536  clh 30781  cltrn 30898  ctrl 30955  cdia 31826 This theorem is referenced by:  dian0  31837  diatrl  31842  dialss  31844  diaglbN  31853  dibelval3  31945  dibopelval3  31946  diblss  31968 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-rep 4320  ax-sep 4330  ax-nul 4338  ax-pr 4403 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 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-disoa 31827
 Copyright terms: Public domain W3C validator