HSE Home Hilbert Space Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HSE Home  >  Th. List  >  qlaxr4i Unicode version

Theorem qlaxr4i 22985
Description: One of the conditions showing  CH is an ortholattice. (This corresponds to axiom "ax-r4" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlaxr4.1  |-  A  e. 
CH
qlaxr4.2  |-  B  e. 
CH
qlaxr4.3  |-  A  =  B
Assertion
Ref Expression
qlaxr4i  |-  ( _|_ `  A )  =  ( _|_ `  B )

Proof of Theorem qlaxr4i
StepHypRef Expression
1 qlaxr4.3 . 2  |-  A  =  B
21fveq2i 5672 1  |-  ( _|_ `  A )  =  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1649    e. wcel 1717   ` cfv 5395   CHcch 22281   _|_cort 22282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-rex 2656  df-rab 2659  df-v 2902  df-dif 3267  df-un 3269  df-in 3271  df-ss 3278  df-nul 3573  df-if 3684  df-sn 3764  df-pr 3765  df-op 3767  df-uni 3959  df-br 4155  df-iota 5359  df-fv 5403
  Copyright terms: Public domain W3C validator