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Theorem chjcomi 22972
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 22732 . 2  |-  A  e.  SH
3 chjcl.2 . . 3  |-  B  e. 
CH
43chshii 22732 . 2  |-  B  e.  SH
52, 4shjcomi 22875 1  |-  ( A  vH  B )  =  ( B  vH  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1653    e. wcel 1726  (class class class)co 6083   CHcch 22434    vH chj 22438
This theorem is referenced by:  chub2i  22974  chnlei  22989  chj12i  23026  lejdiri  23043  cmcm2i  23097  cmbr3i  23104  qlax2i  23132  osumcor2i  23148  3oalem5  23170  pjcji  23188  mayetes3i  23234  mdslj2i  23825  mdsl1i  23826  cvmdi  23829  mdslmd2i  23835  mdexchi  23840  cvexchi  23874  atabsi  23906  mdsymlem1  23908  mdsymlem6  23913  mdsymlem8  23915  sumdmdlem2  23924  dmdbr5ati  23927
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405  ax-hilex 22504
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fv 5464  df-ov 6086  df-oprab 6087  df-mpt2 6088  df-sh 22711  df-ch 22726  df-chj 22814
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