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Theorem chjvali 28914
Description: Value of join in C. (Contributed by NM, 9-Aug-2000.) (New usage is discouraged.)
Hypotheses
Ref Expression
chjval.1 𝐴C
chjval.2 𝐵C
Assertion
Ref Expression
chjvali (𝐴 𝐵) = (⊥‘(⊥‘(𝐴𝐵)))

Proof of Theorem chjvali
StepHypRef Expression
1 chjval.1 . 2 𝐴C
2 chjval.2 . 2 𝐵C
3 chjval 28913 . 2 ((𝐴C𝐵C ) → (𝐴 𝐵) = (⊥‘(⊥‘(𝐴𝐵))))
41, 2, 3mp2an 679 1 (𝐴 𝐵) = (⊥‘(⊥‘(𝐴𝐵)))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1507  wcel 2050  cun 3829  cfv 6190  (class class class)co 6978   C cch 28488  cort 28489   chj 28492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-13 2301  ax-ext 2750  ax-sep 5061  ax-nul 5068  ax-pr 5187  ax-hilex 28558
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547  df-eu 2583  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-ral 3093  df-rex 3094  df-rab 3097  df-v 3417  df-sbc 3684  df-dif 3834  df-un 3836  df-in 3838  df-ss 3845  df-nul 4181  df-if 4352  df-pw 4425  df-sn 4443  df-pr 4445  df-op 4449  df-uni 4714  df-br 4931  df-opab 4993  df-id 5313  df-xp 5414  df-rel 5415  df-cnv 5416  df-co 5417  df-dm 5418  df-rn 5419  df-res 5420  df-ima 5421  df-iota 6154  df-fun 6192  df-fv 6198  df-ov 6981  df-oprab 6982  df-mpo 6983  df-sh 28766  df-ch 28780  df-chj 28871
This theorem is referenced by:  chj0i  29016  sshhococi  29107
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