Metamath Proof Explorer
Description: The covers relation is not reflexive. (Contributed by NM, 26-Jun-2004)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
cvnref |
⊢ ( 𝐴 ∈ Cℋ → ¬ 𝐴 ⋖ℋ 𝐴 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
cvnsym |
⊢ ( ( 𝐴 ∈ Cℋ ∧ 𝐴 ∈ Cℋ ) → ( 𝐴 ⋖ℋ 𝐴 → ¬ 𝐴 ⋖ℋ 𝐴 ) ) |
2 |
1
|
anidms |
⊢ ( 𝐴 ∈ Cℋ → ( 𝐴 ⋖ℋ 𝐴 → ¬ 𝐴 ⋖ℋ 𝐴 ) ) |
3 |
2
|
pm2.01d |
⊢ ( 𝐴 ∈ Cℋ → ¬ 𝐴 ⋖ℋ 𝐴 ) |