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Theorem qlaxr2i 27658
Description: One of the conditions showing C 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 𝐴C
qlaxr2.2 𝐵C
qlaxr2.3 𝐶C
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 2536 1 𝐴 = 𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1938   C cch 26952
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-ext 2494
This theorem depends on definitions:  df-bi 195  df-cleq 2507
This theorem is referenced by: (None)
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