Metamath Proof Explorer


Theorem prstcocval

Description: Orthocomplementation is unchanged. (Contributed by Zhi Wang, 20-Sep-2024) (Proof shortened by AV, 12-Nov-2024)

Ref Expression
Hypotheses prstcnid.c No typesetting found for |- ( ph -> C = ( ProsetToCat ` K ) ) with typecode |-
prstcnid.k φKProset
prstcoc.oc φ˙=ocK
Assertion prstcocval φ˙=ocC

Proof

Step Hyp Ref Expression
1 prstcnid.c Could not format ( ph -> C = ( ProsetToCat ` K ) ) : No typesetting found for |- ( ph -> C = ( ProsetToCat ` K ) ) with typecode |-
2 prstcnid.k φKProset
3 prstcoc.oc φ˙=ocK
4 ocid oc=Slotocndx
5 slotsdifocndx ocndxcompndxocndxHomndx
6 5 simpli ocndxcompndx
7 5 simpri ocndxHomndx
8 1 2 4 6 7 prstcnid φocK=ocC
9 3 8 eqtrd φ˙=ocC