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Theorem qlaxr2i 22228
Description: One of the conditions showing  CH is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlaxr2.1  |-  A  e. 
CH
qlaxr2.2  |-  B  e. 
CH
qlaxr2.3  |-  C  e. 
CH
qlaxr2.4  |-  A  =  B
qlaxr2.5  |-  B  =  C
Assertion
Ref Expression
qlaxr2i  |-  A  =  C

Proof of Theorem qlaxr2i
StepHypRef Expression
1 qlaxr2.4 . 2  |-  A  =  B
2 qlaxr2.5 . 2  |-  B  =  C
31, 2eqtri 2316 1  |-  A  =  C
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696   CHcch 21525
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-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-cleq 2289
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