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Theorem chjcomi 28667
Description: Commutative law for join in C. (Contributed by NM, 14-Oct-1999.) (New usage is discouraged.)
Hypotheses
Ref Expression
ch0le.1 𝐴C
chjcl.2 𝐵C
Assertion
Ref Expression
chjcomi (𝐴 𝐵) = (𝐵 𝐴)

Proof of Theorem chjcomi
StepHypRef Expression
1 ch0le.1 . . 3 𝐴C
21chshii 28424 . 2 𝐴S
3 chjcl.2 . . 3 𝐵C
43chshii 28424 . 2 𝐵S
52, 4shjcomi 28570 1 (𝐴 𝐵) = (𝐵 𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  wcel 2145  (class class class)co 6796   C cch 28126   chj 28130
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4916  ax-nul 4924  ax-pr 5035  ax-hilex 28196
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-eu 2622  df-mo 2623  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3353  df-sbc 3588  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4227  df-pw 4300  df-sn 4318  df-pr 4320  df-op 4324  df-uni 4576  df-br 4788  df-opab 4848  df-id 5158  df-xp 5256  df-rel 5257  df-cnv 5258  df-co 5259  df-dm 5260  df-rn 5261  df-res 5262  df-ima 5263  df-iota 5993  df-fun 6032  df-fv 6038  df-ov 6799  df-oprab 6800  df-mpt2 6801  df-sh 28404  df-ch 28418  df-chj 28509
This theorem is referenced by:  chub2i  28669  chnlei  28684  chj12i  28721  lejdiri  28738  cmcm2i  28792  cmbr3i  28799  qlax2i  28827  osumcor2i  28843  3oalem5  28865  pjcji  28883  mayetes3i  28928  mdslj2i  29519  mdsl1i  29520  cvmdi  29523  mdslmd2i  29529  mdexchi  29534  cvexchi  29568  atabsi  29600  mdsymlem1  29602  mdsymlem6  29607  mdsymlem8  29609  sumdmdlem2  29618  dmdbr5ati  29621
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