Metamath Proof Explorer
Description: CH join is an upper bound of two elements. (Contributed by NM, 5-Nov-2000) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ch0le.1 |
⊢ 𝐴 ∈ Cℋ |
|
|
chjcl.2 |
⊢ 𝐵 ∈ Cℋ |
|
Assertion |
chub2i |
⊢ 𝐴 ⊆ ( 𝐵 ∨ℋ 𝐴 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ch0le.1 |
⊢ 𝐴 ∈ Cℋ |
2 |
|
chjcl.2 |
⊢ 𝐵 ∈ Cℋ |
3 |
1 2
|
chub1i |
⊢ 𝐴 ⊆ ( 𝐴 ∨ℋ 𝐵 ) |
4 |
1 2
|
chjcomi |
⊢ ( 𝐴 ∨ℋ 𝐵 ) = ( 𝐵 ∨ℋ 𝐴 ) |
5 |
3 4
|
sseqtri |
⊢ 𝐴 ⊆ ( 𝐵 ∨ℋ 𝐴 ) |