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Metamath Proof Explorer

Theorem univ

Description: The union of the universe is the universe. Exercise 4.12(c) of Mendelson p. 235. (Contributed by NM, 14-Sep-2003)

		Ref	Expression
	Assertion	univ	$⊢ ⋃ V = V$

Step	Hyp	Ref	Expression
1		pwv	$⊢ 𝒫 V = V$
2	1	unieqi	$⊢ ⋃ 𝒫 V = ⋃ V$
3		unipw	$⊢ ⋃ 𝒫 V = V$
4	2 3	eqtr3i	$⊢ ⋃ V = V$