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Theorem chjvali 25933
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 25932 . 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 1374    e. wcel 1762    u. cun 3467   ` cfv 5579  (class class class)co 6275   CHcch 25508   _|_cort 25509    vH chj 25512
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-sep 4561  ax-nul 4569  ax-pr 4679  ax-hilex 25578
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2272  df-mo 2273  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3108  df-sbc 3325  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-if 3933  df-pw 4005  df-sn 4021  df-pr 4023  df-op 4027  df-uni 4239  df-br 4441  df-opab 4499  df-id 4788  df-xp 4998  df-rel 4999  df-cnv 5000  df-co 5001  df-dm 5002  df-rn 5003  df-res 5004  df-ima 5005  df-iota 5542  df-fun 5581  df-fv 5587  df-ov 6278  df-oprab 6279  df-mpt2 6280  df-sh 25786  df-ch 25801  df-chj 25890
This theorem is referenced by:  chj0i  26035  sshhococi  26126
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