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Theorem chm0i 22841
Description: Meet with Hilbert lattice zero. (Contributed by NM, 6-Aug-2004.) (New usage is discouraged.)
Hypothesis
Ref Expression
ch0le.1  |-  A  e. 
CH
Assertion
Ref Expression
chm0i  |-  ( A  i^i  0H )  =  0H

Proof of Theorem chm0i
StepHypRef Expression
1 inss2 3506 . 2  |-  ( A  i^i  0H )  C_  0H
2 ch0le.1 . . . 4  |-  A  e. 
CH
32ch0lei 22802 . . 3  |-  0H  C_  A
4 ssid 3311 . . 3  |-  0H  C_  0H
53, 4ssini 3508 . 2  |-  0H  C_  ( A  i^i  0H )
61, 5eqssi 3308 1  |-  ( A  i^i  0H )  =  0H
Colors of variables: wff set class
Syntax hints:    = wceq 1649    e. wcel 1717    i^i cin 3263   CHcch 22281   0Hc0h 22287
This theorem is referenced by:  chm0  22842
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369  ax-sep 4272  ax-hilex 22351
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-rex 2656  df-rab 2659  df-v 2902  df-dif 3267  df-un 3269  df-in 3271  df-ss 3278  df-nul 3573  df-if 3684  df-pw 3745  df-sn 3764  df-pr 3765  df-op 3767  df-uni 3959  df-br 4155  df-opab 4209  df-xp 4825  df-cnv 4827  df-dm 4829  df-rn 4830  df-res 4831  df-ima 4832  df-iota 5359  df-fv 5403  df-ov 6024  df-sh 22558  df-ch 22573  df-ch0 22604
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