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Mirrors > Home > HSE Home > Th. List > qlaxr4i | Structured version Visualization version GIF version |
Description: One of the conditions showing Cℋ is an ortholattice. (This corresponds to axiom "ax-r4" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
qlaxr4.1 | ⊢ 𝐴 ∈ Cℋ |
qlaxr4.2 | ⊢ 𝐵 ∈ Cℋ |
qlaxr4.3 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
qlaxr4i | ⊢ (⊥‘𝐴) = (⊥‘𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlaxr4.3 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | 1 | fveq2i 6335 | 1 ⊢ (⊥‘𝐴) = (⊥‘𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1631 ∈ wcel 2145 ‘cfv 6031 Cℋ cch 28126 ⊥cort 28127 |
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 |
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-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-rex 3067 df-rab 3070 df-v 3353 df-dif 3726 df-un 3728 df-in 3730 df-ss 3737 df-nul 4064 df-if 4226 df-sn 4317 df-pr 4319 df-op 4323 df-uni 4575 df-br 4787 df-iota 5994 df-fv 6039 |
This theorem is referenced by: (None) |
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