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Theorem qlax2i 27653
 Description: One of the equations showing Cℋ is an ortholattice. (This corresponds to axiom "ax-2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlax.1 𝐴C
qlax.2 𝐵C
Assertion
Ref Expression
qlax2i (𝐴 𝐵) = (𝐵 𝐴)

Proof of Theorem qlax2i
StepHypRef Expression
1 qlax.1 . 2 𝐴C
2 qlax.2 . 2 𝐵C
31, 2chjcomi 27493 1 (𝐴 𝐵) = (𝐵 𝐴)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1474   ∈ wcel 1938  (class class class)co 6431   Cℋ cch 26952   ∨ℋ chj 26956 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-9 1947  ax-10 1966  ax-11 1971  ax-12 1983  ax-13 2137  ax-ext 2494  ax-sep 4607  ax-nul 4616  ax-pr 4732  ax-hilex 27022 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-eu 2366  df-mo 2367  df-clab 2501  df-cleq 2507  df-clel 2510  df-nfc 2644  df-ral 2805  df-rex 2806  df-rab 2809  df-v 3079  df-sbc 3307  df-dif 3447  df-un 3449  df-in 3451  df-ss 3458  df-nul 3778  df-if 3940  df-pw 4013  df-sn 4029  df-pr 4031  df-op 4035  df-uni 4271  df-br 4482  df-opab 4542  df-id 4847  df-xp 4938  df-rel 4939  df-cnv 4940  df-co 4941  df-dm 4942  df-rn 4943  df-res 4944  df-ima 4945  df-iota 5658  df-fun 5696  df-fv 5702  df-ov 6434  df-oprab 6435  df-mpt2 6436  df-sh 27230  df-ch 27244  df-chj 27335 This theorem is referenced by: (None)
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