Theorem olop 37228

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 37226	. 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
2	1	simprbi 497	1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP)

Syntax hints:   → wi 4   ∈ wcel 2106  Latclat 18149  OPcops 37186  OLcol 37188

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ol 37192

This theorem is referenced by:  olposN  37229  oldmm1  37231  oldmm2  37232  oldmm3N  37233  oldmm4  37234  oldmj1  37235  oldmj2  37236  oldmj3  37237  oldmj4  37238  olj01  37239  olj02  37240  olm11  37241  olm12  37242  latmassOLD  37243  olm01  37250  olm02  37251  omlop  37255  meetat  37310  hlop  37376  polatN  37945