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Mirrors > Home > HSE Home > Th. List > chjvali | Structured version Visualization version GIF version |
Description: Value of join in Cℋ. (Contributed by NM, 9-Aug-2000.) (New usage is discouraged.) |
Ref | Expression |
---|---|
chjval.1 | ⊢ 𝐴 ∈ Cℋ |
chjval.2 | ⊢ 𝐵 ∈ Cℋ |
Ref | Expression |
---|---|
chjvali | ⊢ (𝐴 ∨ℋ 𝐵) = (⊥‘(⊥‘(𝐴 ∪ 𝐵))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chjval.1 | . 2 ⊢ 𝐴 ∈ Cℋ | |
2 | chjval.2 | . 2 ⊢ 𝐵 ∈ Cℋ | |
3 | chjval 27595 | . 2 ⊢ ((𝐴 ∈ Cℋ ∧ 𝐵 ∈ Cℋ ) → (𝐴 ∨ℋ 𝐵) = (⊥‘(⊥‘(𝐴 ∪ 𝐵)))) | |
4 | 1, 2, 3 | mp2an 704 | 1 ⊢ (𝐴 ∨ℋ 𝐵) = (⊥‘(⊥‘(𝐴 ∪ 𝐵))) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∈ wcel 1977 ∪ cun 3538 ‘cfv 5804 (class class class)co 6549 Cℋ cch 27170 ⊥cort 27171 ∨ℋ chj 27174 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 ax-hilex 27240 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-mo 2463 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-rab 2905 df-v 3175 df-sbc 3403 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-pw 4110 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-opab 4644 df-id 4953 df-xp 5044 df-rel 5045 df-cnv 5046 df-co 5047 df-dm 5048 df-rn 5049 df-res 5050 df-ima 5051 df-iota 5768 df-fun 5806 df-fv 5812 df-ov 6552 df-oprab 6553 df-mpt2 6554 df-sh 27448 df-ch 27462 df-chj 27553 |
This theorem is referenced by: chj0i 27698 sshhococi 27789 |
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