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Metamath Proof Explorer

Theorem hashin

Description: The size of the intersection of a set and a class is less than or equal to the size of the set. (Contributed by AV, 4-Jan-2021)

		Ref	Expression
	Assertion	hashin	$⊢ A \in V \to \|A \cap B\| \leq \|A\|$

Step	Hyp	Ref	Expression
1		inss1	$⊢ A \cap B \subseteq A$
2		hashss	$⊢ (A \in V \land A \cap B \subseteq A) \to \|A \cap B\| \leq \|A\|$
3	1 2	mpan2	$⊢ A \in V \to \|A \cap B\| \leq \|A\|$