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Theorem qlax2i 29978
Description: One of the equations showing C 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 29818 1 (𝐴 𝐵) = (𝐵 𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2110  (class class class)co 7269   C cch 29279   chj 29283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2711  ax-sep 5227  ax-nul 5234  ax-pr 5356  ax-hilex 29349
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-nf 1791  df-sb 2072  df-mo 2542  df-eu 2571  df-clab 2718  df-cleq 2732  df-clel 2818  df-nfc 2891  df-ral 3071  df-rex 3072  df-rab 3075  df-v 3433  df-sbc 3721  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-pw 4541  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4846  df-br 5080  df-opab 5142  df-id 5489  df-xp 5595  df-rel 5596  df-cnv 5597  df-co 5598  df-dm 5599  df-rn 5600  df-res 5601  df-ima 5602  df-iota 6389  df-fun 6433  df-fv 6439  df-ov 7272  df-oprab 7273  df-mpo 7274  df-sh 29557  df-ch 29571  df-chj 29660
This theorem is referenced by: (None)
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