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Theorem qlaxr4i 29715
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 6720 1 (⊥‘𝐴) = (⊥‘𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1543  wcel 2110  cfv 6380   C cch 29010  cort 29011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3070  df-v 3410  df-dif 3869  df-un 3871  df-in 3873  df-ss 3883  df-nul 4238  df-if 4440  df-sn 4542  df-pr 4544  df-op 4548  df-uni 4820  df-br 5054  df-iota 6338  df-fv 6388
This theorem is referenced by: (None)
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