Theorem ficardid

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

	Ref	Expression
Assertion	ficardid	|- ( A e. Fin -> ( card ` A ) ~~ A )

Proof

Step	Hyp	Ref	Expression
1		finnum	|- ( A e. Fin -> A e. dom card )
2		cardid2	|- ( A e. dom card -> ( card ` A ) ~~ A )
3	1 2	syl	|- ( A e. Fin -> ( card ` A ) ~~ A )