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Metamath Proof Explorer

Theorem ficardid

Description: A finite set is equinumerous to its cardinal number. (Contributed by Mario Carneiro, 21-Sep-2013)

		Ref	Expression
	Assertion	ficardid	$⊢ A \in Fin \to card (A) \approx A$

Step	Hyp	Ref	Expression
1		finnum	$⊢ A \in Fin \to A \in dom card$
2		cardid2	$⊢ A \in dom card \to card (A) \approx A$
3	1 2	syl	$⊢ A \in Fin \to card (A) \approx A$