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Metamath Proof Explorer

Theorem chjidmi

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

		Ref	Expression
	Hypothesis	chjidm.1	$⊢ A \in C_{ℋ}$
	Assertion	chjidmi	$⊢ A \lor_{ℋ} A = A$

Step	Hyp	Ref	Expression
1		chjidm.1	$⊢ A \in C_{ℋ}$
2		chjidm	$⊢ A \in C_{ℋ} \to A \lor_{ℋ} A = A$
3	1 2	ax-mp	$⊢ A \lor_{ℋ} A = A$