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Theorem chjcomi 29172
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 28931 . 2 𝐴S
3 chjcl.2 . . 3 𝐵C
43chshii 28931 . 2 𝐵S
52, 4shjcomi 29075 1 (𝐴 𝐵) = (𝐵 𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  wcel 2105  (class class class)co 7145   C cch 28633   chj 28637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790  ax-sep 5194  ax-nul 5201  ax-pr 5320  ax-hilex 28703
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-mo 2615  df-eu 2647  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ral 3140  df-rex 3141  df-rab 3144  df-v 3494  df-sbc 3770  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-pw 4537  df-sn 4558  df-pr 4560  df-op 4564  df-uni 4831  df-br 5058  df-opab 5120  df-id 5453  df-xp 5554  df-rel 5555  df-cnv 5556  df-co 5557  df-dm 5558  df-rn 5559  df-res 5560  df-ima 5561  df-iota 6307  df-fun 6350  df-fv 6356  df-ov 7148  df-oprab 7149  df-mpo 7150  df-sh 28911  df-ch 28925  df-chj 29014
This theorem is referenced by:  chub2i  29174  chnlei  29189  chj12i  29226  lejdiri  29243  cmcm2i  29297  cmbr3i  29304  qlax2i  29332  osumcor2i  29348  3oalem5  29370  pjcji  29388  mayetes3i  29433  mdslj2i  30024  mdsl1i  30025  cvmdi  30028  mdslmd2i  30034  mdexchi  30039  cvexchi  30073  atabsi  30105  mdsymlem1  30107  mdsymlem6  30112  mdsymlem8  30114  sumdmdlem2  30123  dmdbr5ati  30126
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