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Metamath Proof Explorer

Theorem fnbigcup

Description: Bigcup is a function over the universal class. (Contributed by Scott Fenton, 11-Apr-2012)

		Ref	Expression
	Assertion	fnbigcup	$⊢ 𝖡𝗂𝗀𝖼𝗎𝗉 Fn V$

Step	Hyp	Ref	Expression
1		fobigcup	$⊢ 𝖡𝗂𝗀𝖼𝗎𝗉 : V \underset{onto}{⟶} V$
2		fofn	$⊢ 𝖡𝗂𝗀𝖼𝗎𝗉 : V \underset{onto}{⟶} V \to 𝖡𝗂𝗀𝖼𝗎𝗉 Fn V$
3	1 2	ax-mp	$⊢ 𝖡𝗂𝗀𝖼𝗎𝗉 Fn V$