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Theorem qlaxr4i 31662
Description: One of the conditions showing C 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 𝐴C
qlaxr4.2 𝐵C
qlaxr4.3 𝐴 = 𝐵
Assertion
Ref Expression
qlaxr4i (⊥‘𝐴) = (⊥‘𝐵)

Proof of Theorem qlaxr4i
StepHypRef Expression
1 qlaxr4.3 . 2 𝐴 = 𝐵
21fveq2i 6909 1 (⊥‘𝐴) = (⊥‘𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1536  wcel 2105  cfv 6562   C cch 30957  cort 30958
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4912  df-br 5148  df-iota 6515  df-fv 6570
This theorem is referenced by: (None)
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