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Theorem chjcomi 29258
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 29017 . 2 𝐴S
3 chjcl.2 . . 3 𝐵C
43chshii 29017 . 2 𝐵S
52, 4shjcomi 29161 1 (𝐴 𝐵) = (𝐵 𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  wcel 2115  (class class class)co 7149   C cch 28719   chj 28723
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317  ax-hilex 28789
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-rab 3142  df-v 3482  df-sbc 3759  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-pw 4524  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5053  df-opab 5115  df-id 5447  df-xp 5548  df-rel 5549  df-cnv 5550  df-co 5551  df-dm 5552  df-rn 5553  df-res 5554  df-ima 5555  df-iota 6302  df-fun 6345  df-fv 6351  df-ov 7152  df-oprab 7153  df-mpo 7154  df-sh 28997  df-ch 29011  df-chj 29100
This theorem is referenced by:  chub2i  29260  chnlei  29275  chj12i  29312  lejdiri  29329  cmcm2i  29383  cmbr3i  29390  qlax2i  29418  osumcor2i  29434  3oalem5  29456  pjcji  29474  mayetes3i  29519  mdslj2i  30110  mdsl1i  30111  cvmdi  30114  mdslmd2i  30120  mdexchi  30125  cvexchi  30159  atabsi  30191  mdsymlem1  30193  mdsymlem6  30198  mdsymlem8  30200  sumdmdlem2  30209  dmdbr5ati  30212
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