This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fingch

Description: A finite set is a GCH-set. (Contributed by Mario Carneiro, 15-May-2015)

		Ref	Expression
	Assertion	fingch	$⊢ Fin \subseteq GCH$

Step	Hyp	Ref	Expression
1		ssun1	$⊢ Fin \subseteq Fin \cup \{x \| \forall y \neg (x ≺ y \land y ≺ 𝒫 x)\}$
2		df-gch	$⊢ GCH = Fin \cup \{x \| \forall y \neg (x ≺ y \land y ≺ 𝒫 x)\}$
3	1 2	sseqtrri	$⊢ Fin \subseteq GCH$