Theorem chjvali

Description: Value of join in CH . (Contributed by NM, 9-Aug-2000) (New usage is discouraged.)

	Ref	Expression
Hypotheses	chjval.1	⊢ 𝐴 ∈ Cℋ
	chjval.2	⊢ 𝐵 ∈ Cℋ
Assertion	chjvali	⊢ ( 𝐴 ∨ℋ 𝐵 ) = ( ⊥ ‘ ( ⊥ ‘ ( 𝐴 ∪ 𝐵 ) ) )

Proof

Step	Hyp	Ref	Expression
1		chjval.1	⊢ 𝐴 ∈ Cℋ
2		chjval.2	⊢ 𝐵 ∈ Cℋ
3		chjval	⊢ ( ( 𝐴 ∈ Cℋ ∧ 𝐵 ∈ Cℋ ) → ( 𝐴 ∨ℋ 𝐵 ) = ( ⊥ ‘ ( ⊥ ‘ ( 𝐴 ∪ 𝐵 ) ) ) )
4	1 2 3	mp2an	⊢ ( 𝐴 ∨ℋ 𝐵 ) = ( ⊥ ‘ ( ⊥ ‘ ( 𝐴 ∪ 𝐵 ) ) )