Theorem ollat 34500

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

Assertion

Ref	Expression
ollat	|- ( K e. OL -> K e. Lat )

Proof of Theorem ollat

Step	Hyp	Ref	Expression
1		isolat 34499	. 2 |- ( K e. OL <-> ( K e. Lat /\ K e. OP ) )
2	1	simplbi 476	1 |- ( K e. OL -> K e. Lat )

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:  oldmm1  34504  oldmj1  34508  olj01  34512  olj02  34513  olm12  34515  latmassOLD  34516  latm12  34517  latm32  34518  latmrot  34519  latm4  34520  latmmdiN  34521  latmmdir  34522  olm01  34523  olm02  34524  omllat  34529  meetat  34583