Theorem chm1 9379

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 2230	. 2 |- (A i^i H~) (_ A
2		ssid 2080	. . 3 |- A (_ A
3		ch0le.1	. . . 4 |- A e. CH
4	3	chssi 9101	. . 3 |- A (_ H~
5	2, 4	ssini 2233	. 2 |- A (_ (A i^i H~)
6	1, 5	eqssi 2078	1 |- (A i^i H~) = A

Syntax hints:   = wceq 956   e. wcel 958   i^i cin 2046  H~chil 8788  CHcch 8798

This theorem is referenced by:  stcltrlem1 10203

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-sh 9076  df-ch 9092

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