Theorem chm0 9413

Description: Meet with Hilbert lattice zero.

Hypothesis

Ref	Expression
ch0le.1	|- A e. CH

Assertion

Ref	Expression
chm0	|- (A i^i 0H) = 0H

Proof of Theorem chm0

Step	Hyp	Ref	Expression
1		inss2 2231	. 2 |- (A i^i 0H) (_ 0H
2		ch0le.1	. . . 4 |- A e. CH
3	2	ch0le 9374	. . 3 |- 0H (_ A
4		ssid 2080	. . 3 |- 0H (_ 0H
5	3, 4	ssini 2233	. 2 |- 0H (_ (A i^i 0H)
6	1, 5	eqssi 2078	1 |- (A i^i 0H) = 0H

Syntax hints:   = wceq 956   e. wcel 958   i^i cin 2046  CHcch 8798  0Hc0h 8804

This theorem is referenced by:  chm0t 9414

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-sep 2703  ax-hilex 8869

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-ral 1649  df-v 1812  df-in 2051  df-ss 2053  df-sn 2412  df-sh 9076  df-ch 9092  df-ch0 9125

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