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Metamath Proof Explorer

Theorem pwuni

Description: A class is a subclass of the power class of its union. Exercise 6(b) of Enderton p. 38. (Contributed by NM, 14-Oct-1996)

		Ref	Expression
	Assertion	pwuni	$⊢ A \subseteq 𝒫 ⋃ A$

Step	Hyp	Ref	Expression
1		elssuni	$⊢ x \in A \to x \subseteq ⋃ A$
2		velpw	$⊢ x \in 𝒫 ⋃ A \leftrightarrow x \subseteq ⋃ A$
3	1 2	sylibr	$⊢ x \in A \to x \in 𝒫 ⋃ A$
4	3	ssriv	$⊢ A \subseteq 𝒫 ⋃ A$