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

Theorem qlaxr4i 22213
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 5528 1  |-  ( _|_ `  A )  =  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. wcel 1684   ` cfv 5255   CHcch 21509   _|_cort 21510
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263
  Copyright terms: Public domain W3C validator