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Theorem qlaxr5i 29070
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 6934 1 (𝐴 𝐶) = (𝐵 𝐶)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1601  wcel 2107  (class class class)co 6924   C cch 28362   chj 28366
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-rex 3096  df-rab 3099  df-v 3400  df-dif 3795  df-un 3797  df-in 3799  df-ss 3806  df-nul 4142  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-uni 4674  df-br 4889  df-iota 6101  df-fv 6145  df-ov 6927
This theorem is referenced by: (None)
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