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Mirrors > Home > HSE Home > Th. List > qlax2i | Structured version Visualization version GIF version |
Description: One of the equations showing Cℋ is an ortholattice. (This corresponds to axiom "ax-2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
qlax.1 | ⊢ 𝐴 ∈ Cℋ |
qlax.2 | ⊢ 𝐵 ∈ Cℋ |
Ref | Expression |
---|---|
qlax2i | ⊢ (𝐴 ∨ℋ 𝐵) = (𝐵 ∨ℋ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlax.1 | . 2 ⊢ 𝐴 ∈ Cℋ | |
2 | qlax.2 | . 2 ⊢ 𝐵 ∈ Cℋ | |
3 | 1, 2 | chjcomi 29818 | 1 ⊢ (𝐴 ∨ℋ 𝐵) = (𝐵 ∨ℋ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∈ wcel 2110 (class class class)co 7269 Cℋ cch 29279 ∨ℋ chj 29283 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2015 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2158 ax-12 2175 ax-ext 2711 ax-sep 5227 ax-nul 5234 ax-pr 5356 ax-hilex 29349 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3an 1088 df-tru 1545 df-fal 1555 df-ex 1787 df-nf 1791 df-sb 2072 df-mo 2542 df-eu 2571 df-clab 2718 df-cleq 2732 df-clel 2818 df-nfc 2891 df-ral 3071 df-rex 3072 df-rab 3075 df-v 3433 df-sbc 3721 df-dif 3895 df-un 3897 df-in 3899 df-ss 3909 df-nul 4263 df-if 4466 df-pw 4541 df-sn 4568 df-pr 4570 df-op 4574 df-uni 4846 df-br 5080 df-opab 5142 df-id 5489 df-xp 5595 df-rel 5596 df-cnv 5597 df-co 5598 df-dm 5599 df-rn 5600 df-res 5601 df-ima 5602 df-iota 6389 df-fun 6433 df-fv 6439 df-ov 7272 df-oprab 7273 df-mpo 7274 df-sh 29557 df-ch 29571 df-chj 29660 |
This theorem is referenced by: (None) |
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