Theorem chm1 9374

Description: Meet with lattice one in CH.

Hypothesis

Ref	Expression
ch0le.1	|- A e. CH

Assertion

Ref	Expression
chm1	|- (A i^i H~) = A

Proof of Theorem chm1

Step	Hyp	Ref	Expression
1		inss1 2233	. 2 |- (A i^i H~) (_ A
2		ssid 2083	. . 3 |- A (_ A
3		ch0le.1	. . . 4 |- A e. CH
4	3	chssi 9096	. . 3 |- A (_ H~
5	2, 4	ssini 2236	. 2 |- A (_ (A i^i H~)
6	1, 5	eqssi 2081	1 |- (A i^i H~) = A

Syntax hints:   = wceq 958   e. wcel 960   i^i cin 2049  H~chil 8783  CHcch 8793

This theorem is referenced by:  stcltrlem1 10198

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462  ax-sep 2708  ax-hilex 8864

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-ral 1652  df-v 1815  df-in 2054  df-ss 2056  df-sh 9071  df-ch 9087

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