Theorem olop 38816

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

Assertion

Ref	Expression
olop	⊢ (𝐾 ∈ OL → 𝐾 ∈ OP)

Proof of Theorem olop

Step	Hyp	Ref	Expression
1		isolat 38814	. 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
2	1	simprbi 495	1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP)

Syntax hints:   → wi 4   ∈ wcel 2098  Latclat 18426  OPcops 38774  OLcol 38776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-in 3951  df-ol 38780

This theorem is referenced by:  olposN  38817  oldmm1  38819  oldmm2  38820  oldmm3N  38821  oldmm4  38822  oldmj1  38823  oldmj2  38824  oldmj3  38825  oldmj4  38826  olj01  38827  olj02  38828  olm11  38829  olm12  38830  latmassOLD  38831  olm01  38838  olm02  38839  omlop  38843  meetat  38898  hlop  38964  polatN  39534