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Theorem chjcomi 22962
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 22722 . 2  |-  A  e.  SH
3 chjcl.2 . . 3  |-  B  e. 
CH
43chshii 22722 . 2  |-  B  e.  SH
52, 4shjcomi 22865 1  |-  ( A  vH  B )  =  ( B  vH  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725  (class class class)co 6073   CHcch 22424    vH chj 22428
This theorem is referenced by:  chub2i  22964  chnlei  22979  chj12i  23016  lejdiri  23033  cmcm2i  23087  cmbr3i  23094  qlax2i  23122  osumcor2i  23138  3oalem5  23160  pjcji  23178  mayetes3i  23224  mdslj2i  23815  mdsl1i  23816  cvmdi  23819  mdslmd2i  23825  mdexchi  23830  cvexchi  23864  atabsi  23896  mdsymlem1  23898  mdsymlem6  23903  mdsymlem8  23905  sumdmdlem2  23914  dmdbr5ati  23917
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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-hilex 22494
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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fv 5454  df-ov 6076  df-oprab 6077  df-mpt2 6078  df-sh 22701  df-ch 22716  df-chj 22804
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