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Metamath Proof Explorer

Theorem chjcomi

Description: Commutative law for join in CH . (Contributed by NM, 14-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1 ⊢ 𝐴 ∈ Cℋ
chjcl.2 ⊢ 𝐵 ∈ Cℋ
Assertion chjcomi ( 𝐴 ∨ℋ 𝐵 ) = ( 𝐵 ∨ℋ 𝐴 )

Proof

Step Hyp Ref Expression
1 ch0le.1 ⊢ 𝐴 ∈ Cℋ
2 chjcl.2 ⊢ 𝐵 ∈ Cℋ
3 1 chshii ⊢ 𝐴 ∈ Sℋ
4 2 chshii ⊢ 𝐵 ∈ Sℋ
5 3 4 shjcomi ⊢ ( 𝐴 ∨ℋ 𝐵 ) = ( 𝐵 ∨ℋ 𝐴 )