Theorem chjidmi

Description: Idempotent law for Hilbert lattice join. (Contributed by NM, 15-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Hypothesis	chjidm.1	⊢ 𝐴 ∈ Cℋ
Assertion	chjidmi	⊢ ( 𝐴 ∨ℋ 𝐴 ) = 𝐴

Proof

Step	Hyp	Ref	Expression
1		chjidm.1	⊢ 𝐴 ∈ Cℋ
2		chjidm	⊢ ( 𝐴 ∈ Cℋ → ( 𝐴 ∨ℋ 𝐴 ) = 𝐴 )
3	1 2	ax-mp	⊢ ( 𝐴 ∨ℋ 𝐴 ) = 𝐴