![]() |
Hilbert Space Explorer |
< Previous
Next >
Nearby theorems |
|
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 7422 | 1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1540 ∈ wcel 2105 (class class class)co 7412 Cℋ cch 30616 ∨ℋ chj 30620 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-rab 3432 df-v 3475 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-iota 6495 df-fv 6551 df-ov 7415 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |