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Theorem chjval 26942
Description: Value of join in  CH. (Contributed by NM, 9-Aug-2000.) (New usage is discouraged.)
Assertion
Ref Expression
chjval  |-  ( ( A  e.  CH  /\  B  e.  CH )  ->  ( A  vH  B
)  =  ( _|_ `  ( _|_ `  ( A  u.  B )
) ) )

Proof of Theorem chjval
StepHypRef Expression
1 chsh 26814 . 2  |-  ( A  e.  CH  ->  A  e.  SH )
2 chsh 26814 . 2  |-  ( B  e.  CH  ->  B  e.  SH )
3 shjval 26941 . 2  |-  ( ( A  e.  SH  /\  B  e.  SH )  ->  ( A  vH  B
)  =  ( _|_ `  ( _|_ `  ( A  u.  B )
) ) )
41, 2, 3syl2an 479 1  |-  ( ( A  e.  CH  /\  B  e.  CH )  ->  ( A  vH  B
)  =  ( _|_ `  ( _|_ `  ( A  u.  B )
) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370    = wceq 1437    e. wcel 1872    u. cun 3372   ` cfv 5539  (class class class)co 6244   SHcsh 26518   CHcch 26519   _|_cort 26520    vH chj 26523
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2403  ax-sep 4484  ax-nul 4493  ax-pr 4598  ax-hilex 26589
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2275  df-mo 2276  df-clab 2410  df-cleq 2416  df-clel 2419  df-nfc 2553  df-ne 2596  df-ral 2714  df-rex 2715  df-rab 2718  df-v 3019  df-sbc 3238  df-dif 3377  df-un 3379  df-in 3381  df-ss 3388  df-nul 3700  df-if 3850  df-pw 3921  df-sn 3937  df-pr 3939  df-op 3943  df-uni 4158  df-br 4362  df-opab 4421  df-id 4706  df-xp 4797  df-rel 4798  df-cnv 4799  df-co 4800  df-dm 4801  df-rn 4802  df-res 4803  df-ima 4804  df-iota 5503  df-fun 5541  df-fv 5547  df-ov 6247  df-oprab 6248  df-mpt2 6249  df-sh 26797  df-ch 26811  df-chj 26900
This theorem is referenced by:  chjvali  26943
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