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Theorem chjcomi 28167
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 27924 . 2 𝐴S
3 chjcl.2 . . 3 𝐵C
43chshii 27924 . 2 𝐵S
52, 4shjcomi 28070 1 (𝐴 𝐵) = (𝐵 𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  wcel 1992  (class class class)co 6605   C cch 27626   chj 27630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606  ax-sep 4746  ax-nul 4754  ax-pr 4872  ax-hilex 27696
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-eu 2478  df-mo 2479  df-clab 2613  df-cleq 2619  df-clel 2622  df-nfc 2756  df-ral 2917  df-rex 2918  df-rab 2921  df-v 3193  df-sbc 3423  df-dif 3563  df-un 3565  df-in 3567  df-ss 3574  df-nul 3897  df-if 4064  df-pw 4137  df-sn 4154  df-pr 4156  df-op 4160  df-uni 4408  df-br 4619  df-opab 4679  df-id 4994  df-xp 5085  df-rel 5086  df-cnv 5087  df-co 5088  df-dm 5089  df-rn 5090  df-res 5091  df-ima 5092  df-iota 5813  df-fun 5852  df-fv 5858  df-ov 6608  df-oprab 6609  df-mpt2 6610  df-sh 27904  df-ch 27918  df-chj 28009
This theorem is referenced by:  chub2i  28169  chnlei  28184  chj12i  28221  lejdiri  28238  cmcm2i  28292  cmbr3i  28299  qlax2i  28327  osumcor2i  28343  3oalem5  28365  pjcji  28383  mayetes3i  28428  mdslj2i  29019  mdsl1i  29020  cvmdi  29023  mdslmd2i  29029  mdexchi  29034  cvexchi  29068  atabsi  29100  mdsymlem1  29102  mdsymlem6  29107  mdsymlem8  29109  sumdmdlem2  29118  dmdbr5ati  29121
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