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Theorem qlaxr4i 22207
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 5490 1  |-  ( _|_ `  A )  =  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1625    e. wcel 1687   ` cfv 5223   CHcch 21503   _|_cort 21504
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1638  ax-8 1646  ax-6 1706  ax-7 1711  ax-11 1718  ax-12 1870  ax-ext 2267
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 938  df-tru 1312  df-ex 1531  df-nf 1534  df-sb 1633  df-clab 2273  df-cleq 2279  df-clel 2282  df-nfc 2411  df-rex 2552  df-rab 2555  df-v 2793  df-dif 3158  df-un 3160  df-in 3162  df-ss 3169  df-nul 3459  df-if 3569  df-sn 3649  df-pr 3650  df-op 3652  df-uni 3831  df-br 4027  df-opab 4081  df-xp 4696  df-cnv 4698  df-dm 4700  df-rn 4701  df-res 4702  df-ima 4703  df-fv 5231
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