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Theorem chjvali 21948
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 21947 . 2  |-  ( ( A  e.  CH  /\  B  e.  CH )  ->  ( A  vH  B
)  =  ( _|_ `  ( _|_ `  ( A  u.  B )
) ) )
41, 2, 3mp2an 653 1  |-  ( A  vH  B )  =  ( _|_ `  ( _|_ `  ( A  u.  B ) ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696    u. cun 3163   ` cfv 5271  (class class class)co 5874   CHcch 21525   _|_cort 21526    vH chj 21529
This theorem is referenced by:  chj0i  22050  sshhococi  22141
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230  ax-hilex 21595
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fun 5273  df-fv 5279  df-ov 5877  df-oprab 5878  df-mpt2 5879  df-sh 21802  df-ch 21817  df-chj 21905
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