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Theorem chle0 22898
 Description: No Hilbert lattice element is smaller than zero. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.)
Assertion
Ref Expression
chle0

Proof of Theorem chle0
StepHypRef Expression
1 chsh 22680 . 2
2 shle0 22897 . 2
31, 2syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1649   wcel 1721   wss 3280  csh 22384  cch 22385  c0h 22391 This theorem is referenced by:  chle0i  22907  chssoc  22951  hatomistici  23818  atcvat4i  23853 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-hilex 22455 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-pw 3761  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-opab 4227  df-xp 4843  df-cnv 4845  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850  df-iota 5377  df-fv 5421  df-ov 6043  df-sh 22662  df-ch 22677  df-ch0 22708
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