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Theorem chm0i 30474
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 4194 . 2 (𝐴 ∩ 0) ⊆ 0
2 ch0le.1 . . . 4 𝐴C
32ch0lei 30435 . . 3 0𝐴
4 ssid 3971 . . 3 0 ⊆ 0
53, 4ssini 4196 . 2 0 ⊆ (𝐴 ∩ 0)
61, 5eqssi 3965 1 (𝐴 ∩ 0) = 0
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2107  cin 3914   C cch 29913  0c0h 29919
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-sep 5261  ax-hilex 29983
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-if 4492  df-pw 4567  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4871  df-br 5111  df-opab 5173  df-xp 5644  df-cnv 5646  df-dm 5648  df-rn 5649  df-res 5650  df-ima 5651  df-iota 6453  df-fv 6509  df-ov 7365  df-sh 30191  df-ch 30205  df-ch0 30237
This theorem is referenced by:  chm0  30475
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