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Theorem chjcomi 22043
Description: Commutative law for join in  CH. (Contributed by NM, 14-Oct-1999.) (New usage is discouraged.)
Hypotheses
Ref Expression
ch0le.1  |-  A  e. 
CH
chjcl.2  |-  B  e. 
CH
Assertion
Ref Expression
chjcomi  |-  ( A  vH  B )  =  ( B  vH  A
)

Proof of Theorem chjcomi
StepHypRef Expression
1 ch0le.1 . . 3  |-  A  e. 
CH
21chshii 21803 . 2  |-  A  e.  SH
3 chjcl.2 . . 3  |-  B  e. 
CH
43chshii 21803 . 2  |-  B  e.  SH
52, 4shjcomi 21946 1  |-  ( A  vH  B )  =  ( B  vH  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. wcel 1685  (class class class)co 5820   CHcch 21505    vH chj 21509
This theorem is referenced by:  chub2i  22045  chnlei  22060  chj12i  22097  lejdiri  22114  cmcm2i  22168  cmbr3i  22175  qlax2i  22203  osumcor2i  22219  3oalem5  22241  pjcji  22259  mayetes3i  22305  mdslj2i  22896  mdsl1i  22897  cvmdi  22900  mdslmd2i  22906  mdexchi  22911  cvexchi  22945  atabsi  22977  mdsymlem1  22979  mdsymlem6  22984  mdsymlem8  22986  sumdmdlem2  22995  dmdbr5ati  22998
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-13 1687  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pr 4213  ax-un 4511  ax-hilex 21575
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1631  df-eu 2148  df-mo 2149  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-rab 2553  df-v 2791  df-sbc 2993  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-if 3567  df-pw 3628  df-sn 3647  df-pr 3648  df-op 3650  df-uni 3829  df-br 4025  df-opab 4079  df-id 4308  df-xp 4694  df-rel 4695  df-cnv 4696  df-co 4697  df-dm 4698  df-rn 4699  df-res 4700  df-ima 4701  df-fun 5223  df-fv 5229  df-ov 5823  df-oprab 5824  df-mpt2 5825  df-sh 21782  df-ch 21797  df-chj 21885
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