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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 7414 | 1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2098 (class class class)co 7404 Cℋ cch 30687 ∨ℋ 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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