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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 31277 | . 2 ⊢ ((𝐴 ∈ Cℋ ∧ 𝐵 ∈ Cℋ ) → (𝐴 ∨ℋ 𝐵) = (⊥‘(⊥‘(𝐴 ∪ 𝐵)))) | |
4 | 1, 2, 3 | mp2an 690 | 1 ⊢ (𝐴 ∨ℋ 𝐵) = (⊥‘(⊥‘(𝐴 ∪ 𝐵))) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2098 ∪ cun 3944 ‘cfv 6553 (class class class)co 7423 Cℋ cch 30854 ⊥cort 30855 ∨ℋ chj 30858 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5303 ax-nul 5310 ax-pr 5432 ax-hilex 30924 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2930 df-ral 3051 df-rex 3060 df-rab 3419 df-v 3463 df-sbc 3776 df-dif 3949 df-un 3951 df-in 3953 df-ss 3963 df-nul 4325 df-if 4533 df-pw 4608 df-sn 4633 df-pr 4635 df-op 4639 df-uni 4913 df-br 5153 df-opab 5215 df-id 5579 df-xp 5687 df-rel 5688 df-cnv 5689 df-co 5690 df-dm 5691 df-rn 5692 df-res 5693 df-ima 5694 df-iota 6505 df-fun 6555 df-fv 6561 df-ov 7426 df-oprab 7427 df-mpo 7428 df-sh 31132 df-ch 31146 df-chj 31235 |
This theorem is referenced by: chj0i 31380 sshhococi 31471 |
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