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Theorem chjvali 24893
Description: Value of join in  CH. (Contributed by NM, 9-Aug-2000.) (New usage is discouraged.)
Hypotheses
Ref Expression
chjval.1  |-  A  e. 
CH
chjval.2  |-  B  e. 
CH
Assertion
Ref Expression
chjvali  |-  ( A  vH  B )  =  ( _|_ `  ( _|_ `  ( A  u.  B ) ) )

Proof of Theorem chjvali
StepHypRef Expression
1 chjval.1 . 2  |-  A  e. 
CH
2 chjval.2 . 2  |-  B  e. 
CH
3 chjval 24892 . 2  |-  ( ( A  e.  CH  /\  B  e.  CH )  ->  ( A  vH  B
)  =  ( _|_ `  ( _|_ `  ( A  u.  B )
) ) )
41, 2, 3mp2an 672 1  |-  ( A  vH  B )  =  ( _|_ `  ( _|_ `  ( A  u.  B ) ) )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370    e. wcel 1758    u. cun 3426   ` cfv 5518  (class class class)co 6192   CHcch 24468   _|_cort 24469    vH chj 24472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4513  ax-nul 4521  ax-pr 4631  ax-hilex 24538
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3072  df-sbc 3287  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-nul 3738  df-if 3892  df-pw 3962  df-sn 3978  df-pr 3980  df-op 3984  df-uni 4192  df-br 4393  df-opab 4451  df-id 4736  df-xp 4946  df-rel 4947  df-cnv 4948  df-co 4949  df-dm 4950  df-rn 4951  df-res 4952  df-ima 4953  df-iota 5481  df-fun 5520  df-fv 5526  df-ov 6195  df-oprab 6196  df-mpt2 6197  df-sh 24746  df-ch 24761  df-chj 24850
This theorem is referenced by:  chj0i  24995  sshhococi  25086
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