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Mirrors > Home > HSE Home > Th. List > qlaxr5i | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
qlaxr5.1 | ⊢ 𝐴 ∈ Cℋ |
qlaxr5.2 | ⊢ 𝐵 ∈ Cℋ |
qlaxr5.3 | ⊢ 𝐶 ∈ Cℋ |
qlaxr5.4 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
qlaxr5i | ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlaxr5.4 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | 1 | oveq1i 7440 | 1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 ∈ wcel 2105 (class class class)co 7430 Cℋ cch 30957 ∨ℋ chj 30961 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1539 df-fal 1549 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-rab 3433 df-v 3479 df-dif 3965 df-un 3967 df-ss 3979 df-nul 4339 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-uni 4912 df-br 5148 df-iota 6515 df-fv 6570 df-ov 7433 |
This theorem is referenced by: (None) |
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