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Theorem chjval 29133
Description: Value of join in C. (Contributed by NM, 9-Aug-2000.) (New usage is discouraged.)
Assertion
Ref Expression
chjval ((𝐴C𝐵C ) → (𝐴 𝐵) = (⊥‘(⊥‘(𝐴𝐵))))

Proof of Theorem chjval
StepHypRef Expression
1 chsh 29005 . 2 (𝐴C𝐴S )
2 chsh 29005 . 2 (𝐵C𝐵S )
3 shjval 29132 . 2 ((𝐴S𝐵S ) → (𝐴 𝐵) = (⊥‘(⊥‘(𝐴𝐵))))
41, 2, 3syl2an 598 1 ((𝐴C𝐵C ) → (𝐴 𝐵) = (⊥‘(⊥‘(𝐴𝐵))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399   = wceq 1538  wcel 2114  cun 3906  cfv 6334  (class class class)co 7140   S csh 28709   C cch 28710  cort 28711   chj 28714
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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794  ax-sep 5179  ax-nul 5186  ax-pr 5307  ax-hilex 28780
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 2070  df-mo 2622  df-eu 2653  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-ral 3135  df-rex 3136  df-rab 3139  df-v 3471  df-sbc 3748  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4266  df-if 4440  df-pw 4513  df-sn 4540  df-pr 4542  df-op 4546  df-uni 4814  df-br 5043  df-opab 5105  df-id 5437  df-xp 5538  df-rel 5539  df-cnv 5540  df-co 5541  df-dm 5542  df-rn 5543  df-res 5544  df-ima 5545  df-iota 6293  df-fun 6336  df-fv 6342  df-ov 7143  df-oprab 7144  df-mpo 7145  df-sh 28988  df-ch 29002  df-chj 29091
This theorem is referenced by:  chjvali  29134
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