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Metamath Proof Explorer

Theorem chub2

Description: Hilbert lattice join is greater than or equal to its second argument. (Contributed by NM, 12-Jun-2004) (New usage is discouraged.)

		Ref	Expression
	Assertion	chub2	$⊢ (A \in C_{ℋ} \land B \in C_{ℋ}) \to A \subseteq B \lor_{ℋ} A$

Step	Hyp	Ref	Expression
1		chub1	$⊢ (A \in C_{ℋ} \land B \in C_{ℋ}) \to A \subseteq A \lor_{ℋ} B$
2		chjcom	$⊢ (A \in C_{ℋ} \land B \in C_{ℋ}) \to A \lor_{ℋ} B = B \lor_{ℋ} A$
3	1 2	sseqtrd	$⊢ (A \in C_{ℋ} \land B \in C_{ℋ}) \to A \subseteq B \lor_{ℋ} A$