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Theorem chm1i 22090
Description: Meet with lattice one in  CH. (Contributed by NM, 24-Oct-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
ch0le.1  |-  A  e. 
CH
Assertion
Ref Expression
chm1i  |-  ( A  i^i  ~H )  =  A

Proof of Theorem chm1i
StepHypRef Expression
1 ch0le.1 . . 3  |-  A  e. 
CH
21chssii 21866 . 2  |-  A  C_  ~H
3 df-ss 3200 . 2  |-  ( A 
C_  ~H  <->  ( A  i^i  ~H )  =  A )
42, 3mpbi 199 1  |-  ( A  i^i  ~H )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1633    e. wcel 1701    i^i cin 3185    C_ wss 3186   ~Hchil 21554   CHcch 21564
This theorem is referenced by:  stcltrlem1  22911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178  ax-hilex 21634
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-rex 2583  df-rab 2586  df-v 2824  df-dif 3189  df-un 3191  df-in 3193  df-ss 3200  df-nul 3490  df-if 3600  df-pw 3661  df-sn 3680  df-pr 3681  df-op 3683  df-uni 3865  df-br 4061  df-opab 4115  df-xp 4732  df-cnv 4734  df-dm 4736  df-rn 4737  df-res 4738  df-ima 4739  df-iota 5256  df-fv 5300  df-ov 5903  df-sh 21841  df-ch 21856
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