Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  qlaxr5i Structured version   Visualization version   GIF version

Theorem qlaxr5i 29462
 Description: One of the conditions showing Cℋ is an ortholattice. (This corresponds to axiom "ax-r5" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlaxr5.1 𝐴C
qlaxr5.2 𝐵C
qlaxr5.3 𝐶C
qlaxr5.4 𝐴 = 𝐵
Assertion
Ref Expression
qlaxr5i (𝐴 𝐶) = (𝐵 𝐶)

Proof of Theorem qlaxr5i
StepHypRef Expression
1 qlaxr5.4 . 2 𝐴 = 𝐵
21oveq1i 7155 1 (𝐴 𝐶) = (𝐵 𝐶)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∈ wcel 2111  (class class class)co 7145   Cℋ cch 28756   ∨ℋ chj 28760 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-un 3888  df-in 3890  df-ss 3900  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4805  df-br 5035  df-iota 6291  df-fv 6340  df-ov 7148 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator