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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 6675 | 1 ⊢ (⊥‘𝐴) = (⊥‘𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∈ wcel 2114 ‘cfv 6357 Cℋ cch 28708 ⊥cort 28709 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-br 5069 df-iota 6316 df-fv 6365 |
This theorem is referenced by: (None) |
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