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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 28667 | 1 ⊢ (𝐴 ∨ℋ 𝐵) = (𝐵 ∨ℋ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1631 ∈ wcel 2145 (class class class)co 6793 Cℋ cch 28126 ∨ℋ chj 28130 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 ax-sep 4915 ax-nul 4923 ax-pr 5034 ax-hilex 28196 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 837 df-3an 1073 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-eu 2622 df-mo 2623 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-ral 3066 df-rex 3067 df-rab 3070 df-v 3353 df-sbc 3588 df-dif 3726 df-un 3728 df-in 3730 df-ss 3737 df-nul 4064 df-if 4226 df-pw 4299 df-sn 4317 df-pr 4319 df-op 4323 df-uni 4575 df-br 4787 df-opab 4847 df-id 5157 df-xp 5255 df-rel 5256 df-cnv 5257 df-co 5258 df-dm 5259 df-rn 5260 df-res 5261 df-ima 5262 df-iota 5994 df-fun 6033 df-fv 6039 df-ov 6796 df-oprab 6797 df-mpt2 6798 df-sh 28404 df-ch 28418 df-chj 28509 |
This theorem is referenced by: (None) |
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