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Theorem qlaxr5i 23129
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  |-  A  e. 
CH
qlaxr5.2  |-  B  e. 
CH
qlaxr5.3  |-  C  e. 
CH
qlaxr5.4  |-  A  =  B
Assertion
Ref Expression
qlaxr5i  |-  ( A  vH  C )  =  ( B  vH  C
)

Proof of Theorem qlaxr5i
StepHypRef Expression
1 qlaxr5.4 . 2  |-  A  =  B
21oveq1i 6083 1  |-  ( A  vH  C )  =  ( B  vH  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725  (class class class)co 6073   CHcch 22424    vH chj 22428
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076
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