Theorem olop 33519

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 33517	. 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
2	1	simprbi 479	1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP)

Syntax hints:   → wi 4   ∈ wcel 1977  Latclat 16868  OPcops 33477  OLcol 33479

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-in 3547  df-ol 33483

This theorem is referenced by:  olposN  33520  oldmm1  33522  oldmm2  33523  oldmm3N  33524  oldmm4  33525  oldmj1  33526  oldmj2  33527  oldmj3  33528  oldmj4  33529  olj01  33530  olj02  33531  olm11  33532  olm12  33533  latmassOLD  33534  olm01  33541  olm02  33542  omlop  33546  meetat  33601  hlop  33667  polatN  34235