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Theorem chm0i 31372
Description: Meet with Hilbert lattice zero. (Contributed by NM, 6-Aug-2004.) (New usage is discouraged.)
Hypothesis
Ref Expression
ch0le.1 𝐴C
Assertion
Ref Expression
chm0i (𝐴 ∩ 0) = 0

Proof of Theorem chm0i
StepHypRef Expression
1 inss2 4228 . 2 (𝐴 ∩ 0) ⊆ 0
2 ch0le.1 . . . 4 𝐴C
32ch0lei 31333 . . 3 0𝐴
4 ssid 3999 . . 3 0 ⊆ 0
53, 4ssini 4230 . 2 0 ⊆ (𝐴 ∩ 0)
61, 5eqssi 3993 1 (𝐴 ∩ 0) = 0
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  cin 3943   C cch 30811  0c0h 30817
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696  ax-sep 5300  ax-hilex 30881
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rab 3419  df-v 3463  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4323  df-if 4531  df-pw 4606  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4910  df-br 5150  df-opab 5212  df-xp 5684  df-cnv 5686  df-dm 5688  df-rn 5689  df-res 5690  df-ima 5691  df-iota 6501  df-fv 6557  df-ov 7422  df-sh 31089  df-ch 31103  df-ch0 31135
This theorem is referenced by:  chm0  31373
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