Theorem olop 29709

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 29707	. 2 |- ( K e. OL <-> ( K e. Lat /\ K e. OP ) )
2	1	simprbi 451	1 |- ( K e. OL -> K e. OP )

Syntax hints:   -> wi 4   e. wcel 1721   Latclat 14437   OPcops 29667   OLcol 29669

This theorem is referenced by:  olposN  29710  oldmm1  29712  oldmm2  29713  oldmm3N  29714  oldmm4  29715  oldmj1  29716  oldmj2  29717  oldmj3  29718  oldmj4  29719  olj01  29720  olj02  29721  olm11  29722  olm12  29723  latmassOLD  29724  olm01  29731  olm02  29732  omlop  29736  meetat  29791  hlop  29857  polatN  30425

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 2393

This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-in 3295  df-ol 29673