HSE Home Hilbert Space Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HSE Home  >  Th. List  >  qlaxr2i Structured version   Visualization version   GIF version

Theorem qlaxr2i 28832
Description: One of the conditions showing C is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlaxr2.1 𝐴C
qlaxr2.2 𝐵C
qlaxr2.3 𝐶C
qlaxr2.4 𝐴 = 𝐵
qlaxr2.5 𝐵 = 𝐶
Assertion
Ref Expression
qlaxr2i 𝐴 = 𝐶

Proof of Theorem qlaxr2i
StepHypRef Expression
1 qlaxr2.4 . 2 𝐴 = 𝐵
2 qlaxr2.5 . 2 𝐵 = 𝐶
31, 2eqtri 2793 1 𝐴 = 𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  wcel 2145   C cch 28126
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-cleq 2764
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator