Hilbert Space Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > HSE Home > Th. List > qlaxr2i | Structured version Visualization version GIF version |
Description: One of the conditions showing Cℋ is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
qlaxr2.1 | ⊢ 𝐴 ∈ Cℋ |
qlaxr2.2 | ⊢ 𝐵 ∈ Cℋ |
qlaxr2.3 | ⊢ 𝐶 ∈ Cℋ |
qlaxr2.4 | ⊢ 𝐴 = 𝐵 |
qlaxr2.5 | ⊢ 𝐵 = 𝐶 |
Ref | Expression |
---|---|
qlaxr2i | ⊢ 𝐴 = 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlaxr2.4 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | qlaxr2.5 | . 2 ⊢ 𝐵 = 𝐶 | |
3 | 1, 2 | eqtri 2842 | 1 ⊢ 𝐴 = 𝐶 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1531 ∈ wcel 2108 Cℋ cch 28698 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-9 2118 ax-ext 2791 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1775 df-cleq 2812 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |