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Theorem chm0i 28958
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 4126 . 2 (𝐴 ∩ 0) ⊆ 0
2 ch0le.1 . . . 4 𝐴C
32ch0lei 28919 . . 3 0𝐴
4 ssid 3910 . . 3 0 ⊆ 0
53, 4ssini 4128 . 2 0 ⊆ (𝐴 ∩ 0)
61, 5eqssi 3905 1 (𝐴 ∩ 0) = 0
Colors of variables: wff setvar class
Syntax hints:   = wceq 1522  wcel 2081  cin 3858   C cch 28397  0c0h 28403
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-10 2112  ax-11 2126  ax-12 2141  ax-ext 2769  ax-sep 5094  ax-hilex 28467
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-3an 1082  df-tru 1525  df-ex 1762  df-nf 1766  df-sb 2043  df-clab 2776  df-cleq 2788  df-clel 2863  df-nfc 2935  df-rex 3111  df-rab 3114  df-v 3439  df-dif 3862  df-un 3864  df-in 3866  df-ss 3874  df-nul 4212  df-if 4382  df-pw 4455  df-sn 4473  df-pr 4475  df-op 4479  df-uni 4746  df-br 4963  df-opab 5025  df-xp 5449  df-cnv 5451  df-dm 5453  df-rn 5454  df-res 5455  df-ima 5456  df-iota 6189  df-fv 6233  df-ov 7019  df-sh 28675  df-ch 28689  df-ch0 28721
This theorem is referenced by:  chm0  28959
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