Theorem olop 34501

Description: An ortholattice is an orthoposet. (Contributed by NM, 18-Sep-2011.)

Assertion

Ref	Expression
olop	|- ( K e. OL -> K e. OP )

Proof of Theorem olop

Step	Hyp	Ref	Expression
1		isolat 34499	. 2 |- ( K e. OL <-> ( K e. Lat /\ K e. OP ) )
2	1	simprbi 480	1 |- ( K e. OL -> K e. OP )

Syntax hints:   -> wi 4   e. wcel 1990   Latclat 17045   OPcops 34459   OLcol 34461

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-in 3581  df-ol 34465

This theorem is referenced by:  olposN  34502  oldmm1  34504  oldmm2  34505  oldmm3N  34506  oldmm4  34507  oldmj1  34508  oldmj2  34509  oldmj3  34510  oldmj4  34511  olj01  34512  olj02  34513  olm11  34514  olm12  34515  latmassOLD  34516  olm01  34523  olm02  34524  omlop  34528  meetat  34583  hlop  34649  polatN  35217