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Theorem qlaxr5i 22986
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 6031 1  |-  ( A  vH  C )  =  ( B  vH  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1649    e. wcel 1717  (class class class)co 6021   CHcch 22281    vH chj 22285
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  df-ov 6024
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