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Theorem qlaxr5i 22230
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 5884 1  |-  ( A  vH  C )  =  ( B  vH  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696  (class class class)co 5874   CHcch 21525    vH chj 21529
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877
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