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Theorem qlaxr5i 31393
Description: One of the conditions showing C 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 7414 1 (𝐴 𝐶) = (𝐵 𝐶)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  (class class class)co 7404   C cch 30687   chj 30691
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-iota 6488  df-fv 6544  df-ov 7407
This theorem is referenced by: (None)
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