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Theorem qlaxr4i 27659
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 5995 1 (⊥‘𝐴) = (⊥‘𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1938  cfv 5694   C cch 26952  cort 26953
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-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-11 1971  ax-12 1983  ax-13 2137  ax-ext 2494
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1699  df-sb 1831  df-clab 2501  df-cleq 2507  df-clel 2510  df-nfc 2644  df-rex 2806  df-rab 2809  df-v 3079  df-dif 3447  df-un 3449  df-in 3451  df-ss 3458  df-nul 3778  df-if 3940  df-sn 4029  df-pr 4031  df-op 4035  df-uni 4271  df-br 4482  df-iota 5658  df-fv 5702
This theorem is referenced by: (None)
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