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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 7441 | 1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶) |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∈ wcel 2108 (class class class)co 7431 Cℋ cch 30948 ∨ℋ chj 30952 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-iota 6514 df-fv 6569 df-ov 7434 |
| This theorem is referenced by: (None) |
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