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Theorem qlaxr1i 28831
Description: One of the conditions showing C is an ortholattice. (This corresponds to axiom "ax-r1" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlaxr1.1 𝐴C
qlaxr1.2 𝐵C
qlaxr1.3 𝐴 = 𝐵
Assertion
Ref Expression
qlaxr1i 𝐵 = 𝐴

Proof of Theorem qlaxr1i
StepHypRef Expression
1 qlaxr1.3 . 2 𝐴 = 𝐵
21eqcomi 2780 1 𝐵 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  wcel 2145   C cch 28126
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-cleq 2764
This theorem is referenced by: (None)
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