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Theorem chm0i 31519
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 4246 . 2 (𝐴 ∩ 0) ⊆ 0
2 ch0le.1 . . . 4 𝐴C
32ch0lei 31480 . . 3 0𝐴
4 ssid 4018 . . 3 0 ⊆ 0
53, 4ssini 4248 . 2 0 ⊆ (𝐴 ∩ 0)
61, 5eqssi 4012 1 (𝐴 ∩ 0) = 0
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  wcel 2106  cin 3962   C cch 30958  0c0h 30964
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-hilex 31028
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-pw 4607  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-xp 5695  df-cnv 5697  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702  df-iota 6516  df-fv 6571  df-ov 7434  df-sh 31236  df-ch 31250  df-ch0 31282
This theorem is referenced by:  chm0  31520
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