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Theorem qlaxr5i 28622
 Description: One of the conditions showing Cℋ is an ortholattice. (This corresponds to axiom "ax-r5" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlaxr5.1 𝐴C
qlaxr5.2 𝐵C
qlaxr5.3 𝐶C
qlaxr5.4 𝐴 = 𝐵
Assertion
Ref Expression
qlaxr5i (𝐴 𝐶) = (𝐵 𝐶)

Proof of Theorem qlaxr5i
StepHypRef Expression
1 qlaxr5.4 . 2 𝐴 = 𝐵
21oveq1i 6700 1 (𝐴 𝐶) = (𝐵 𝐶)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1523   ∈ wcel 2030  (class class class)co 6690   Cℋ cch 27914   ∨ℋ chj 27918 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rex 2947  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-uni 4469  df-br 4686  df-iota 5889  df-fv 5934  df-ov 6693 This theorem is referenced by: (None)
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