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Theorem chjcomi 28899
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 28656 . 2 𝐴S
3 chjcl.2 . . 3 𝐵C
43chshii 28656 . 2 𝐵S
52, 4shjcomi 28802 1 (𝐴 𝐵) = (𝐵 𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1601  wcel 2106  (class class class)co 6922   C cch 28358   chj 28362
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-9 2115  ax-10 2134  ax-11 2149  ax-12 2162  ax-13 2333  ax-ext 2753  ax-sep 5017  ax-nul 5025  ax-pr 5138  ax-hilex 28428
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-mo 2550  df-eu 2586  df-clab 2763  df-cleq 2769  df-clel 2773  df-nfc 2920  df-ral 3094  df-rex 3095  df-rab 3098  df-v 3399  df-sbc 3652  df-dif 3794  df-un 3796  df-in 3798  df-ss 3805  df-nul 4141  df-if 4307  df-pw 4380  df-sn 4398  df-pr 4400  df-op 4404  df-uni 4672  df-br 4887  df-opab 4949  df-id 5261  df-xp 5361  df-rel 5362  df-cnv 5363  df-co 5364  df-dm 5365  df-rn 5366  df-res 5367  df-ima 5368  df-iota 6099  df-fun 6137  df-fv 6143  df-ov 6925  df-oprab 6926  df-mpt2 6927  df-sh 28636  df-ch 28650  df-chj 28741
This theorem is referenced by:  chub2i  28901  chnlei  28916  chj12i  28953  lejdiri  28970  cmcm2i  29024  cmbr3i  29031  qlax2i  29059  osumcor2i  29075  3oalem5  29097  pjcji  29115  mayetes3i  29160  mdslj2i  29751  mdsl1i  29752  cvmdi  29755  mdslmd2i  29761  mdexchi  29766  cvexchi  29800  atabsi  29832  mdsymlem1  29834  mdsymlem6  29839  mdsymlem8  29841  sumdmdlem2  29850  dmdbr5ati  29853
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