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Theorem chjcomi 22049
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 21809 . 2  |-  A  e.  SH
3 chjcl.2 . . 3  |-  B  e. 
CH
43chshii 21809 . 2  |-  B  e.  SH
52, 4shjcomi 21952 1  |-  ( A  vH  B )  =  ( B  vH  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1625    e. wcel 1686  (class class class)co 5860   CHcch 21511    vH chj 21515
This theorem is referenced by:  chub2i  22051  chnlei  22066  chj12i  22103  lejdiri  22120  cmcm2i  22174  cmbr3i  22181  qlax2i  22209  osumcor2i  22225  3oalem5  22247  pjcji  22265  mayetes3i  22311  mdslj2i  22902  mdsl1i  22903  cvmdi  22906  mdslmd2i  22912  mdexchi  22917  cvexchi  22951  atabsi  22983  mdsymlem1  22985  mdsymlem6  22990  mdsymlem8  22992  sumdmdlem2  23001  dmdbr5ati  23004
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-14 1690  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266  ax-sep 4143  ax-nul 4151  ax-pr 4216  ax-hilex 21581
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-eu 2149  df-mo 2150  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ne 2450  df-ral 2550  df-rex 2551  df-rab 2554  df-v 2792  df-sbc 2994  df-dif 3157  df-un 3159  df-in 3161  df-ss 3168  df-nul 3458  df-if 3568  df-pw 3629  df-sn 3648  df-pr 3649  df-op 3651  df-uni 3830  df-br 4026  df-opab 4080  df-id 4311  df-xp 4697  df-rel 4698  df-cnv 4699  df-co 4700  df-dm 4701  df-rn 4702  df-res 4703  df-ima 4704  df-iota 5221  df-fun 5259  df-fv 5265  df-ov 5863  df-oprab 5864  df-mpt2 5865  df-sh 21788  df-ch 21803  df-chj 21891
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